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Call No. ? ^/^/4cession No. // 7 



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M.A., F.R.A.S. 






l<irst Pulltshed in 1927 




THIS brief account of the life and work of Sir 
Isaac Newton does not claim to be a critical 
biography. The author's object has been to 
present the main features of Newton's life and his 
chief contributions to knowledge, in a manner that will 
be understood by a reader who possesses a very 
moderate grounding in the elements of science. Far 
too little attention is paid nowadays to the heroes of 
science, and it is hoped that the present volume will 
help to give to considerable numbers of schoolboys 
and schoolgirls, as well as to children of a larger growth, 
some insight into the life, personality and achieve- 
ments of the greatest man of science England has 

Needless to say the author is indebted to many 
standard books, especially those by Sir David Brewster, 
and to a large number of scattered articles on Newton 
and his work. His thanks are due to Mr. Christopher 
Turnor of Stoke Rochford for kind permission to use 
the marble copy of the famous bust by Roubilliac for 
the frontispiece. 

S. B. 

February, 1927 




II. THE CAMBRIDGE STUDENT, 1661-1665 . 13 


1665 21 


l666 29 


1666 53 

VI. THE OPTICAL DECADE, 1668-1678 . . 62 


VIII. THE " PRINCIPIA," 1687 .... 101 



1696-1727 130 


1727 137 

XII. THE END, 1727 153 

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Rev. Barnabas Smith Hannah 

Robert Barton Hannah ! 


.therine * A Daughter * A 

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.erine Viscount Lymington 
Portsmouth Family 

on's personal estate. 

Newton's family estates at Woolsth 


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SIR ISAAC NEWTON . . . Frontispiece 

From a copy of a bust by Koubtlhac, ^n the possession of 
Christopher Tumor, Esq., at btoke Rochford 



From a drawing by 4. E. Taylor 








8. CAUSE OF PRECESSION . . . . 115 

9. TIDES Il6 


When Newton saw an apple fall, he found 

In that slight startle from his contemplation 

'Tis said (for I'll not answer above ground 
For any sage's creed or calculation) 

A mode of proving that the earth turned round 
In a most natural whirl, called " gravitation " ; 

And this is the sole mortal who could grapple, 

Since Adam, with a fall, or with an apple. 

Man fell with apples, and with apples rose, 
II this be true ; for we must deem the mode 

In which Sir Isaac Newton could disclose 
Through the then unpaved stars the turnpike road, 

A thing to counterbalance human woes : 
For ever since immortal man hath glow'd 

With all kinds of mechanics, and full soon 

Steam-engines will conduct him to the moon. 

LORD BYRON : " Don Juan," 

Canto the Tenth, I and II. 



At first, the Iniant, 

Mewling and pukmg in the nurse's arms. 
And then, the whining School-boy, with his satchel, 
And shining morning face, creeping like snail 
Unwillingly to school. And then, the Lover, 
Sighing like furnace, with a woful ballad 
Made to his mistress' eye-brow. 


IN August, 1642, the sword was drawn in the 
armed struggle between King Charles I and his 
Parliament. For nearly twenty years the struggle 
raged : first the King suffered complete defeat and 
Parliament became the supreme arbiter of the destinies 
of the nation ; then Parliament's power waned and 
became completely subject to the royal will of 
Charles II, restored to the powers and prerogatives of 
his less fortunate father. While the British people was 
in this oscillatory fashion hammering out a form 
of political and social life to express concretely its 
peculiar genius for ordered and law-abiding freedom, 
fully and jealously maintained personal liberty and 
inviolability combined with a dignified acceptance 
of, and submission to, laws derived by common 
consent, there was growing up in its midst a youth 
of unparalleled genius, who was to serve humanity 
in the scientific sphere, but whose life marked an 


epoch in human development as important and as 
significant as any marked by the career of dictator 
or liberator. 

Detached from the great stream of agitated life, 
in the tiny hamlet of Woolsthorpe, in the parish of 
Colsterworth in Lincolnshire, about six miles south 
of Grantham, and a short distance from the main 
north road between London and York, there was born 
in the year of strife 1642 a frail child to a young and 
widowed mother. This child was Isaac Newton. 
When Charles I was executed by his indignant subjects 
and the monarchy gave way to a military common- 
wealth, this little boy was learning in primitive country 
schools the first elements of what was considered to 
be a suitable education for a small farmer. When 
Cromwell had expelled the Long Parliament and had 
been declared Lord High Protector with almost all 
regal powers, young Newton went to Grantham in 
order to continue his education at the King's School. 
Cromwell died when Newton's family had become 
convinced that he would never succeed as a farmer 
and as manager of the paternal estate in Woolsthorpe. 
In 1660, the year of the Stuart restoration and the 
complete subjection of the nation's will to the pre- 
rogative of its refound royal idol, Newton was pre- 
paring for entry upon his studies at Cambridge. The 
mind that was to set free the human intellect for 
unparalleled progress in the elucidation of the secrets 
of nature was approaching maturity, and was about 
to embark on a great adventure of discovery that can 
safely claim to have no superior, perhaps not even a 
rival, in recorded human history. 

Our history books are generally too busy to deal 
with such phenomena. Time was when historical 
records dealt with human heroes rather than with 
human movements. But the heroes held up to popular 
admiration were of other mould than Newton. Warriors 


who had slain, or caused to be slain, their thousands 
and their ten thousands, kings and emperors who used 
peoples and lands as pawns in their game of power and 
empire, royal favourites and jousting nobles all these 
and their myrmidons strutted across the page of 
history ; and if in the mob represented as gazing with 
admiration and envy at the doings of their masters, 
could be discovered a Roger Bacon, a Shakespeare, 
or a Newton, warming themselves in the patronage of 
the great, or struggling with the prejudices and bigotry 
of their rulers, this was sufficient condescension and 
digression from the main object of the narrative. 

Things are indeed different now. The outstanding 
personalities of history are mode to fit into a truer 
picture of general human progress. Popular move- 
ments, national aspirations, industrial development 
and social and political ideology now claim the atten- 
tion of the historian. Yet it is only natural that men 
and women who stood somewhat aside from general 
life, and whose activities did not immediately affect 
national fortunes, should figure but modestly in the 

It is nevertheless a fact that while King and Parlia- 
ment were struggling for supremacy, while Cromwell 
was with dry piety and powder pursuing the fugitive 
remnants of Stuart royalism, while rehabilitated royalty 
was revenging itself on its oppressors, there was emerg- 
ing a power in the intellectual field of human activity 
whose supremacy has been almost unchallenged for 
centuries, and bids fair to remain unchallenged for 
generations to come. 

We all love tales of adventure and stories of derring 
do. But need adventure be conceived as restricted to 
the sphere of physical strife ? When man had to hew 
out for himself a precarious habitation in the primeval 
forest, in the face of inhospitable nature and the 
rivalry of man and beast, the facing of physical danger 


and the unflinching acceptance of personal hazard 
were the supreme virtue, the essential concomitant of 
human survival. Now that the races of humanity 
are still doomed to struggle with one another for the 
possession of the earth, and each race, nation or tribe 
conceives it its first duty to defend its claim to the 
free and undisturbed enjoyment of the fruits of its 
labours, there is virtue in physical prowess and popular 
applause for the heroes of national offence and defence. 
May we not hope for a better day when adventure will 
not connote battle, suffering and death, when human 
conquest will have for its aim the widening of the 
human empire over the forces of nature, when applause 
and admiration will be the reward of intrepid inquiry 
into the physical universe in which we live and thought- 
ful examination of the moral universe that lives 
within us ? 

The heroes of this type of adventure, the warriors 
to whom fall the spoils of such conquest, are at least 
as worthy of our admiration as king and emperor. 
Founders of religious systems and movements, prophets 
and moral teachers of humanity, philosophers and 
scientists, poets and masters of great fiction, have 
moulded human life at least as efficaciously as 
politicians and favourites. There is as much adventure 
in the exercise of the intellectual and spiritual faculties 
as in the exercise of the physical faculties, and there is 
as much romance in the story of these adventures as 
in the narratives of knightly tournaments and martial 

Isaac Newton _was born on December 25, 1642.* 

* Note on the Calendar : The Gregorian calendar was introduced 
in 1582, but was not adopted in Great Britain till 1752. All dates 
given in this book are the contemporary English dates, i.e. in 
accordance with the Julian, or Old Style, calendar. One exception 
will be made. Till 1752 the English new year was on March 25th, 
with the result that, e.g., what was called in England January i, 
1710, was January 12, 1711 in the Gregorian calendar ! It would 


His parentage was undistinguished and of decent 
obscurity not poor but by no means wealthy. The 
father also Isaac Newton belonged to a family that 
had farmed the modest Woolsthorpe estate for several 
generations. The mother Hannah Ayscough came 
from Market-Overton in Rutlandshire. Later in life 
Newton himself had ideas of relationship to some 
Scotch Newtons of noble descent. But this nobility 
was not apparent at his birth. Isaac Newton's father 
died only a few months after the marriage, and several 
months before the birth of his only and posthumous 
child ; the effects on the physical health of the mother 
were sucH that Newton was born prematurely, diminu- 
tive in size and sickly in health. 

Woolsthorpe Manor House, in which Newton was 
born, is still in an excellent state of preservation, 
inhabited by people whose family has resided there for 
several generations. The room in which the birth 
took place is still used as a bedroom, and a tablet over 
the mantelpiece records the birth of Newton with the 
couplet : 

Nature and Nature's laws lay hid in night, 
God said " Let Newton be," and all was light. 

The house is pleasantly situated in a very fertile valley, 
a few minutes from the Parish Church of Colster- 
worth, where the entry of Isaac Newton's baptism on 
January i, 1643, is still to be seen. 

Isaac lived in this house for many years. At first 
he was taken care of by his widowed mother, who also 
had a small estate at Sewstern. But a neighbouring 
clergyman, Rev. Barnabas Smith of North Witham, 

be too confusing to adhere to this practice here, and so our dates will 
be in accordance with the Julian calendar, but with the new year at 
January ist, so that English January i, 1710 corresponds to 
Gregorian January 12, 1710. The difference between the English 
and the Gregorian calendars in Newton's lifetime was ten days till 
February 28, 1 700, and eleven days after this date. 


an old bachelor whom his friends persuaded to marry 
at last, married Newton's mother in 1645. Young 
Isaac's upbringing was then entrusted to his maternal 
grandmother ; he remained at Woolsthorpe while his 
mother was with his stepfather in North Witham. He 
went to small schools at Stoke and Skillington, and 
seems to have enjoyed the care and encouragement of 
his maternal uncle, Rev. W. Ayscough of Burton 
Coggles. Newton's paternal relations were apparently 
but little interested in him till be became famous 
and could be of use to them. A paternal uncle lived 
in Colsterworth, and it was his grandson, John 
Newton, who, as heir-at-law, inherited the estates 
Newton had obtained from his father and mother at 
Woolsthorpe and at Sewstern. This relative was no 
great ornament either to Newton or to humanity. 
He sold the estates to Edmund Turnor of Stoke Koch- 
ford, whose lineal descendants have been the owners 
ofjNewton's birthplace ever since. 

(When Isaac reached the age of twelve he had 
exhausted the very meagre intellectual resources of 
the villages near Woolsthorpe, and in 1655 he was sent 
to the King's School, Grantham J He was not expected 
to walk the six miles to Grantham every day, and so he 
lodged at the house of an apothecary and his wife, 
Mr. and Mrs. Clark, next to the George Hotel in the 
High Street. The house has disappeared, and its site 
is now occupied by an extension of the George Hotel. 
King's School, Grantham, still exists in a modernized 
form, a modest building in pleasant surroundings. 
The Old School, in the form of a small hall, where the 
teaching took place in Newton's time, has been well 
preserved. Its dimensions are 75! feet by 27 feet, 
it has a stage at one end, and is now used for school 
assemblies only. The walls and beams bear witness 
to the proclivities of schoolboys in all generations 
to cut their names wherever possible. Little did 


I. NEWTON, who carved his name on one of the beams 
and his initials on another, realize that he was to carve 
his name in an indelible manner on the walls of the 
temple of fame. 

The head master's house is still used as such, but we 
need conjure up no romantic scenes of youthful genius 
discovered by an admiring and careful mentor. Isaac 
Newton did not at first attract any attention at all. 
He seemed an ordinary boy, perhaps not very strong, 
;and not given to taking any pains to excel in anything. 
We have Newton's own authority for stating that he 
paid little attention to his studies, while at play he 
had not much in common with his schoolfellows. 
There was nothing of the infant prodigy about young 
Isaac : he possessed dormant powers that needed 

It seems absurd to have to say that the awakening 
took the form of a kick in the stomach. A boy who 
ranked higher than Newton in the academic hierarchy 
of the school once caused him considerable pain in this 
way. Newton retaliated in lusty manner, fought his 
assailant till he would fight no more, and duly rubbed 
his nose against the wall of the Grantham Parish 
Church which stands by the school to emphasize 
the victory of revenge. 

Newton was not satisfied with this revenge. His 
enemy stood above him at school, and so Newton was 
determined to vanquish him here too. He finally 
succeeded, and the impulse of the effort carried Newton 
on till he reached the proud position of top boy of the 

For Newton possessed remarkable reserves of mental 
power, and his apparent idleness had been the result 
of his preoccupation with matters in which he was 
more deeply interested. He was low in school at first, 
but when stung to action he soon outstripped all 
competitors. He did not play games with the other 


boys ; but he did better than play games he invented 
new ones. He flew and experimented with kites. 
He was silent and thoughtful in disposition, but 
naughty enough to attach paper lanterns to the kites 
and frighten the simple peasants with the belief that 
they saw those dreadful heavenly visitors comets. 
He was remarkably good with his hands and could 
manipulate tools with great skill, constructing various 
mechanical contrivances, including a windmill model, 
which was made independent of the winds of heaven 
by means of the power supplied by an imprisoned 
mouse. Young Newton was an excellent observer of 
the motions of the heavenly bodies : he made sundials 
which were used for a considerable time one still 
exists in the Parish Church at Colsterworth. He drew 
well and even wrote some indifferent verse. Newton 
was, in a word, a lad of singular ability, doing well 
anything that came his way. 

As we have seen, Newton was not averse to a 
pugilistic encounter when the necessity arose for one, 
but in essence he was gentle and not given to rough 
play. He seems to have preferred the company of 
girl friends to that of boys, and was ever ready to 
render them any service of which he was capable. 

In 1656 Newton's stepfather died. His mother, 
Mrs. Smith, came back to Woolsthorpe, bringing with 
her the three children that had been born to her and 
the Rev. Barnabas Smith. They were two girls and 
a boy : Mary, Benjamin and Hannah Smith. Isaac 
must have contracted a great friendship with his step- 
brother and two stepsisters : all through his life he 
helped them, and he made them his heirs to a very 
considerable personal property. A niece, the daughter 
of Hannah, became a favourite of Newton's later in 
life, and she kept house for him when he lived in 

Newton had reached the top of the school, He was 


as well educated as one could expect to be in those 
rural surroundings. His mother needed a man to 
take charge of the family estates, and what more 
natural than to summon Isaac home and invest him 
with the authority and the responsibilities of this post 
especially as he was the lawful heir to the Wools- 
thorpe manor and had been given the Sewstern estate 
when his mother married Mr. Smith ? The young 
Newton, then in his fifteenth year, came back from 
Grantham. No doubt, if he had been interested in 
farming and grazing, in buying and selling, Newton 
would have made a success of his modest patrimony. 
But the truth is that his interest never wandered in 
the direction of agricultural pursuits. His work on 
and in connexion with the farm was of no real value, 
and it soon became clear that what he hungered for 
was opportunity for academic study and mechanical 

In September, 1658, Oliver Cromwell died. The 
heavens sent a violent storm to signalize this event. 
Instead of seeing to it that the force of the gale shall 
do no damage to the buildings of the farm, to the 
produce and the cattle, Isaac spent his time in jumping 
with the gale and against the gale hoping in this way 
to estimate the force produced by the wind. We can 
conceive with what haste Newton's relatives decided 
that farming was not the vocation to which he was 
born, and how pleased they were to send him back to 
the Grantham school and his boy friends, to the 
apothecary's house and his girl friends. 

There is nothing that canTbe said to characterize 
scientific genius as regards matrimony ; some of the 
world's greatest mathematicians and astronomers 
remained unmarried, others had matrimonial experi- 
ences both happy and unhappy, while still others have 
not been wanting in the spirit of adventure in this 
field. Copernicus was a priestly bachelor. Tycho 


Brahe ran off with the proverbial village maiden and 
led a married life of alternate storm and calm. Kepler 
married twice : he treated the matter of marriage in 
a spirit of business-like caution and achieved an 
imperfect bliss nevertheless. Newton is credited with 
two adventures, both very simple and innocent in 

The apothecary's second wife had a daughter by 
her first husband, Miss Storey by name. She was 
Newton's junior and playfellow, good-looking and 
clever. Apparently Newton's pleasure in the company 
of girl friends developed into something more mature 
in the case of Miss Storey. Butjxjtlj. he and his lady 
friend were not rich enough and not poor enough to 
do' anything improvident. Newton gave up any ideas 
he may have had of married life, and devoted himself 
to his studies. He finally went off to Trinity College, 
Cambridge, on the advice of his uncle from Burton 
Goggles ; Miss Storey stayed in Grantham. Years 
later Newton returned to find her married to another 
(and to yet another !). To his credit be it said that 
Newton retained the memory of his early and tender 
regard for Miss Storey during a long life, and extended 
to her an ever-ready hand of friendship and help. 

Generosity was one of the outstanding features of 
Newton's character all through his life, and he was 
always making gifts or loans to all who needed such 
aid. In a notebook that Newton kept in 1659 we have 
ample evidence of his readiness to help where help was 
needed. We learn that he spent some money on 
" chessemen and dial," while Newton also places on 
record the fact that he spent some money on " china 
ale," "bottled beere/' "sherbet and reaskes," and 
other desiderata of the mortal part of his make-up. 
'(Jrom 1658 to 1661 Newton was at the Grantham 
school preparing for Cambridge? His local reputation 
grew quickly, and when he left school his departure 


was made the occasion of a laudatory address by the 
head master. On June 5, 1661, Isaac Newton, then 
in his nineteenth year, was admitted to Trinity College, 
Cambridge, and embarked upon a career of complete 
devotion to science. 


And soon the flimsy sums he floored, 
And conned the conies thro* and thro*. 
S. K. COWAN : 

" A Supplemental Examination " 

IT has been suggested that the time of reaction and 
repose after violent political convulsion is usually 
characterized by unparalleled progress in science, 
literature and art. The Napoleonic wars were followed 
by great developments in all branches of science in 
Britain, France and Germany, and the recent European 
war has certainly left behind it an interest and an 
activity in science which is producing very fast scientific 
progress in all civilized nations. Whether we have 
here a relationship of cause and effect, whether 
humanity in its best minds, being thoroughly ashamed 
of its recent bestiality, strives to make amends by 
more devout application to the matters of the mind, 
we cannot say. It is certainly of interest that the 
religious convulsions in the England of the middle of 
the sixteenth century were followed by the Elizabethan 
period of drama and literature, white the political 
disturbances of 1642-1660 were followed by one of the 
most brilliant periods of British science, the establish- 
ment of the Royal Society and the foundation of the 
Royal Observatory at Greenwich. 

When Isaac Newton left Woolsthorpe for Cambridge 
his local reputation did not imply that he was really 
a very learned youth. He knew comparatively little, 



especially in mathematics. Other students had done 
more than he. This is, in fact, one of the greatest 
advantages of going to a university like Cambridge. 
He who in his modest home-circle is acclaimed as the 
wise and learned man and excites the admiration of 
his relatives and neighbours, has to submit to com- 
parison with, and the competition of, the best intellects 
brought together from all corners of the land. Wools- 
thorpe, Colsterworth and Grantham could be proud of 
their Isaac, but Cambridge was quite unmoved by. 
Newton's arrival. Other students were at least as far 
advanced in their studies as he, and young Newton 
did not immediately carry off all the prizes within 
his ken. 

This was no real disadvantage to Newton. On the 
contrary, Newton derived considerable benefit from 
his comparatively late development. It is very seldom 
that the youthful prodigy carries out the promise of 
his early achievements. It is not often that the boy 
or girl who is urged on prematurely to advanced studies 
reaches real knowledge and understanding of the 
fundamental ideas involved in these studies. Nature 
does not approve of being hurried. Peaceful bodily 
development accompanied by calm mental growth, 
with no hot-house and artificial forcing, yield the best 
results. The rural surroundings of Newton's early 
years, far from the incitement of intense competition 
and the rush for cheap reputations, enabled him to 
reach healthy mental and physical maturity, untired 
by premature exertions. 

It was an additional advantage to Newton that he 
did not go to the University till well into his nineteenth 
year of age. The modern aspect of university life, 
which is mainly an avenue to the professions, coupled 
with the poverty of most of the students, tends to 
send young boys and girls to the universities when 
they should still be at school. The university is a 


place of independent study within the reach of scholars 
of outstanding merit and authority. For independent 
study an essential desideratum is maturity, culture and 
a sense of responsibility. Newton was not hurried : 
he came to Cambridge just when his intellect was 
arriving at full development. 

The vigour of his intellect was soon displayed to his 
tutors. On more than one occasion he was found to 
have mastered independently treatises that were to 
form the topics of extended lecture courses. The 
result was that he was released from attending such 
courses. He could roam at will in the domains of 
knowledge, and he was soon attracted to the studies 
with which his name was to become immortally 

Kepler's " Optics " is the first book that Newton 
read at Trinity, and as we shall see it was in optics that 
he made some of his first and epoch-making discoveries. 
Attracted by a book on astrology which he picked up 
at a fair held near Cambridge, Newton realized his 
ignorance of geometry. He therefore bought a copy 
of Euclid's " Elements/' It is indeed remarkable that 
he was not led to Euclid in a more direct manner, and, 
further, that he did not realize the genius of the writer 
and the importance of the subject. To his very 
practical mind, not given to idle speculation and 
reaching conclusions by a marvellous insight and 
intuition, Euclid's efforts to prove what appeared to 
be self-evident truths suggested that the author was 
merely trifling a mistake made so often and so 
disastrously in our own generation. Newton suffered 
for this mistake. He entered Trinity as a sizar, a 
class of student then, and till about a century ago, 
required to perform various menial services in return 
for his tuition and necessaries of life, or " commons " 
as they are still called for Newton's mother was not 
rich and he had to use the force of his own intellect 


to raise him in the academic scale. When he competed 
for a scholarship in April, 1664, the examiners, while 
recommending him for an award, commented on his 
poor knowledge of geometry, and Newton was thus 
led to reconsider his opinion of Euclid. 

Newton's interests were indeed hardly those of a 
mathematician as such. (Jlis mind was essentially and 
primarily that of an experimenter^ His school days 
were spent in a manner that suggested the doer rather 
than the thinker, and in the apothecary's house he 
acquired a leaning to alchemy and chemical experi- 
menting. His main incentive to study was his desire 
to understand natural phenomena be they the 
motions of the planets and comets, the periodic flow 
of the tides, the beautiful colours in the spy-glass 
and in soap bubbles, the resistance of the air and the 
laws of motion, the properties of substances and the 
transmutations of the metals. " Observe the products 
of nature in several places, especially in mines . . . 
and if you meet with any transmutations out of their 
own species into another (as out of iron into copper, 
out of any metall into quicksilver, out of one salt into 
another, or into an insipid body, etc.), these, above 
all, will be worth your noting, being the most luciferous, 
and many times lucriferous experiments too in philo- 
sophy." So wrote Newton to a friend a few years after 
his undergraduate days long before he had forsaken 
Cambridge for the London Mint, and gold and silver 
had acquired a personal professional interest for him. 

Cambridge was not then the home of English mathe- 
matics, which flourished rather in Oxford and London. 
It was Newton's own genius that gave to Cambridge its 
mathematical renown. He studied the algebra of his 
time, and the new methods of Rene Descartes, and 
at once began to have ideas wherein lay the germs 
of the binomial theorem and of the differential 


The school boy (or girl) of to-day is taught so well 
that one often wonders if he can learn at all. ["Good 
teaching does not consist in reducing all the ham nuts 
to an amorphous powder, and all the hard crusts to 
soft pap, which can be swallowed without effort, and 
which escape assimilation into the system owing to the 
lack of the saliva of mental effort. The learner must 
learn and not be merely taught ; the effort must be 
his at least as much as the teacher's^ When mathe- 
matical teaching is a careful cataloguing of all possible 
questions that might be invented by evil-minded 
examiners, and literary study has become a careful 
cataloguing of insignificant events in the authors' 
lives, coupled with pathological investigations into 
peculiarities of accidence, syntax and misprints of 
successive editions, who will wonder that grown-up 
Englishmen do not rush to see Shakespeare's 
dramas and do not feel the romance of the binomial 
theorem ? 

- Yet the binomial theorem is full of romance ; it 
throbs with human interest. It is an adventure into 
the unknown. Lead the learner on by judicious 
encouragement to generalize : (i + #) 2 = i + 2* + # 2 , 
(i + %Y = i + 3* + 3* 2 + * 3 > etc., into (i + x) n = 

i + nx + U ^ n """ ' x 2 +...+ nx n ~ l ' + x n , where 


x is any number and n is any positive whole number. 
He cannot but see in this a conquest of territory visible 
to the eye, not mysterious or clothed in the shadows of 
night, but the necessary consolidation of empire, the 
appropriation of lands without which present posses- 
sions are only loosely heldA 

But should not the young learner palpitate with 
excitement when urged to venture into uncharted 
depths and take n to be absolutely anything ? The 
series of terms : 


, n(n i) o , n(n i)(n 2) , 
i + nx + - ' x 2 + ^ ' x* + . . . 

f 1.2 1.2.3 

has no end if n is not a positive whole number : it 
goes on and on and on, indefinitely, to infinity. Does 
this mean anything ? Can, for instance, the square root 
of i + x be as much as a whole and unlimited series 
of terms, all following one another in logical and in- 
exorable law, and taking us who knows whither ? 

We are too civilized in our modern mathematical 
teaching. The ruggednesses are smoothed out, and 
the polished surface thus produced leads to smooth 
and effortless gliding perhaps oftcner to involuntary 
skidding. He will be a benefactor of the race who 
will contrive to bring back into our schools a sense of 
hazard and adventure, the spirit that characterized 
those who made and accumulated the knowledge that 
is taught there. Then we shall no longer suffer the 
boor who claims with pride that he never could under- 
stand mathematics, that lessons on algebra and 
geometry were occasions for inattentiveness, and that 
the binomial theorem is to him merely the topic of 
ignorant jest. 

A great discoverer of our own time has said that *, 
the truly great discoveries are made in early manhood, , 
that he who has passed beyond his thirtieth year , 
without having contributed such discovery to the sum 
of human knowledge, is doomed to go to the grave 
without making any great discovery at all. If true, 
this thought is a sad one. It is, at any rate, remarkable 
that many of the world's most epoch-making discoveries 
fell to the lot of youth and not of old age. Lin the case 
of Isaac Newton, two grand discoveries which have 
rendered his name pre-eminent among all men the 
calculus, and universal gravitation were made in germ 
Long before he reached his thirtieth year, nay, before 
he was twenty-four years of age ; while he discovered 


the spectrum and the true nature of colour before he 
was twenty-eight?} 

TThe binomial theorem, if not so important as his 
omer discoveries, would yet have ensured Newton a 
permanent niche in the temple of fame even if he had 
done nothing else, and this theorem he constructed 
early in 1665, at about the same time as he took the 
degree of Bachelor of Arts, when just over twenty-two 
years okLQ 

Newton's reputation at Trinity was not, however, 
commensurate with his powers and with the things he 
was doing in his study. We have already seen that 
he did not emerge from the scholarship examination 
of 1664 without some censure on the score of inadequate 
geometrical knowledge. His general behaviour was 
not out of the ordinary. He was quite human in his 
pursuits and tastes. He visited the beerhouse, played 
cards for money and lost, and when he went home 
for vacations he brought as presents for his mother 
and stepbrother and stepsisters the same childish gifts 
that the Cambridge man of to-day carries to doting 

We have no information about the order of merit 
of the graduates of 1665. Was Newton the outstand- 
ing graduate of his year? Was he, perhaps, quite 
undistinguished in this examination, without any 
obvious signs of his future in fact, immediately 
emerging greatness ? We cannot tell. We do know 
that he was not elected Fellow at once. He 
was busy with the binomial theorem, he invented 
the method of fluxions his form of the differential 
Calculus he thought about colours and was being led 
to experiment with a prism, within a few months of 
his becoming B. A. Yet he kept all these things to him- 
self. A few notes are extant written in his own hand 
andjcontaining references to these and other matters. 
ButfNewton was never inclined to making public any 


unfinished or half-baked discoveriesj By the time 
that people round him began to suspect that he was 
doing things of value, he was well on the way to 
becoming the great discoverer and original thinker 
that he was soon recognized to be. 


" Line upon line, line upon line ; here a little and there a little." 

Isaiah xxviii, 13 

THE Great Plague broke out in 1665 and spread 
from London to Cambridge. This put an end 
to Newton's regular studies at Trinity, for the 
college authorities decided not to face the risk of the 
pest overtaking them with all the students in residence. 
They therefore dismissed the college on August 8, 1665. 
This went on for practically the whole of the time till 
December of the same year, for the whole of the second 
half of 1666, and for some time in 1667. Newton left 
college in 1665, even before the dismissal in August. 
These two years were thus a time of intermittent 
labour. But we shall soon see that they were by no 
means wasted. 

We have records in Newton's own hand which date 
his pure mathematical progress with considerable 
accuracy. Referring to the winter between 1664 and 
1665, i.e. about the time of his taking the Bachelor's 
degree, Newton says : "At such time I found the 
method of Infinite Series ; and in summer, 1665, 
being forced from Cambridge by the plague, I com- 
puted the area of the Hyperbola at Boothby, in 
Lincolnshire, to two and fifty figures by the same 
method." In a notebook of Newton's we find an 
account of his first discovery of fluxions, written on 
May 20, 1665, and another account with applications 


dated November 13, 1665. Now we know that Newton 
was away from college during the twelve weeks ending 
December 21, 1665. It is therefore clear that he 
made excellent use of his enforced exile from Cam- 

Modern mathematics is unthinkable without the 
calculus. In order to study any natural phenomenon, 
it is essential to deal with the rates of change of various 
quantities. In heat we want to deal with the rate of 
change of temperature, or the rate of heating or 
cooling. In dynamics we have to deal with rate of 
change of position, or the velocity, with rate of change 
of velocity, or the acceleration. In engineering practice 
we have to deal with the rate at which work is being 
done. In pure mathematics the shape of a curve is 
defined by the rate of change of the direction of the 
tangent, while the tangent itself indicates the way 
in which position on the curve changes in terms of 
any two quantities or co-ordinates that define such 

The differential calculus is the branch of mathe- 
matics that deals with such topics. When once the 
suggestion of the fundamental significance of rates has 
been made it becomes clear that progress along this 
direction is an essential condition of progress in science 
at all. Newton realized this, and in his theory of 
fluxions, i.e. the rates of flowing or changing quantities, 
he discovered the N first practical step in the development 
of the calculus. 

A geometrical form of the problem is the following : 
Given a curve drawn on a sheet of paper, how can we 
find its area or the value of any area defined by a 
piece of the curve and straight lines ? This is of 
fundamental importance, for it is soon seen that if we 
plot velocity against time on squared paper, the area 
between the curve thus obtained, the time axis, and 
two ordinates parallel to the velocity axis, gives the 


distance described. The engineer in his indicator 
diagram plots the pressure in the cylinder of his engine 
against the position of the piston : the area of the 
closed curve obtained during a backward and forward 
stroke of the piston gives the work put into the 
machinery by the steam or gases in the cylinder. 

How can such areas be measured ? We can count 
squares and by making the squares small enough we 
can, with sufficient labour, obtain useful results. But 
such a method is only approximate and empirical 
the mathematician would desire, of course, an exact 
solution by calculation. What is the exact area of a 
circle, of an ellipse, of a piece of a parabola cut off by 
any chord, of the space between an hyperbola, an 
asymptote and two lines parallel to the other asymp- 
tote ? How can they be calculated theoretically ? 

The Greeks had faced this problem and applied to 
it their incomparable genius. The method of exhaus- 
tions was invented for the purpose, and in the hands 
of a master like Archimedes yielded useful results. 
The area bounded by a closed curve may be considered 
to lie between the areas of two polygons, one inscribed 
and the other circumscribed to the curve. The greater 
the number of sides in the polygons the closer do their 
areas approach one another, and the more accurately 
therefore can the area of the curve itself be calculated. 
Let the numbers of sides be increased indefinitely. 
The areas of the two polygons approach one another 
indefinitely, giving ultimately the exact area of the 
curve itself. 

Thus, take a circle. Divide its circumference into, 
say, four equal parts at A, B, C, D. Draw the square 
ABCD. Draw the tangents at A, B, C, D : they form 
another square A'B'C'D'. Then the area of the circle 
lies between the; .areas of the two squares. Taking 
the radius to be unity, we at once get that the area of 
a circle of unit radius lies between 2 and 4. Now 



divide the circumference into eight equal parts at 
A, B, C, D, E, F, G, H : we get a regular octagon 
ABCDEFGH inscribed to the circle, while tangents at 
these eight points define another regular octagon, 
A'B'C'D'E'F'G'H', which surrounds the circle. The 
area of the circle lies between the areas of these two 
octagons, i.e. between 2-828 and 3-314. Taking 
sixteen points we get that the area lies between 3*062 




FIG. i 


Squares inscribed and circumscribed 
to circle. 

Octagons inscribed and circumscribed 
to circle. 

and 3- 182. It will be seen how the areas of the polygon 
approach one another, and it will be clear how, pro- 
ceeding in this way, we can, by means of pure calcula- 
tion, reach any degree of accuracy required. 

The area sought for is what mathematicians call w. 
By means of the method of exhaustions Archimedes 
showed that n lies between 3^ and 3yf. 

The area of a piece of a parabola cut off by a chord 
was also obtained and in this case easily and exactly 
by a process based on the same idea. Yet, clever 
though the idea may be, and great the mental vigour 
of the Greeks, only a few cases could be dealt 


with in this way a really practical process did not 

An extension of the area problem is that of finding 
the volume enclosed by a surface. The German, John 
Kepler, of whose work we shall hear more in the sequel, 
was a man of remarkable mathematical genius. Being 
in possession of unexpected money one day, he decided 
to lay down a stock of wine. The wine was to be 
delivered in casks, and naturally the question arose 
as to the volume that is contained by a cask. This 
volume 'depends on the outline of the cask, for a cask 
is approximately defined by the revolution of a curve 
round an axis of symmetry, and Kepler set himself 
the problem of calculating the volume in terms of the 
curve which defines the shape. 

Kepler had some, but not complete, success. Whether 
he ultimately purchased the wine, and whether its 
qualities satisfied his expectations, need not concern 
us now. This incident and Kepler's failure served to 
stimulate the Italian Cavalierijo put forward in 1635 
the epoch-making suggestion,"that an infinite number 
of points make a curve, an infinite number of curves 
make a surface, an infinite number of surfaces make a 
volume. This is not correct logically, and should 
read : a curve consists of an infinite number of infinitely 
short straight lines, a surface consists of an infinite 
number of infinitely narrow strips, a volume consists 
of an infinite number of infinitely thin sheets. But 
Cavalieri's suggestion is one of the most important in 
the history of mathematics, and many useful applica- 
tions of his idea were soon obtained, especially by the 
Frenchman Fermat, some of whose wonderful theorems 
are still puzzling the greatest mathematicians of to- 

No general rule was discovered, however, till the 
Englishman, John Wallis, of Oxford, found one for 
dealing with a whole class of areas, namely, such as 


are defined by curves in which one co-ordinate is 
proportional to a power, like the square or cube, of 
the other co-ordinate. So long as this power was a 
positive whole number no difficulty existed : but when 
the power was negative or fractional Wallis had no 
means of obtaining the exact result. 

Thus, suppose one co-ordinate varies inversely as 
the other, as in the curve given when Robert Boyle 
plotted the volume against the pressure for a perfect 
gas : this curve is called a hyperbola, and this is the 
problem referred to by Newton as having engaged his 
attention when he fled to Boothby, in Lincolnshire, 
because of the plague. The young Newton, then 
twenty-two years of age, found the complete law 
for dealing with any function involving roots of 
complicated expressions, by means of the binomial 

But Newton went further. He realized that 
Cavalieri's ingenious idea contained the germ of some- 
thing far greater. If a curve consists of an infinite 
number of infinitely short lines, cannot the length of 
the curve be considered as growing by the process of 
adding on little line after little line ? If a surface 
consists of an infinite number of infinitely narrow 
strips, cannot the area of the surface be considered as 
growing by the process of adding on narrow strip after 
narrow strip ? If a volume consists of an infinite 
number of infinitely thin sheets, cannot the volume 
be considered as growing by the process of adding on 
thin sheet after thin sheet ? Consider a length, area 
or volume, not as something fixed and dead, cut and 
dried, but as something alive and developing, something 
that varies continuously, as flowing water varies from 
moment to moment : look at it cinematographically 
and not by means of an instantaneous and rigid image 
on a dead screen. 

This is an idea that has changed the face of 


mathematics. The conception of physical quantities, 
including geometrical position, length, etc., as fluent, 
the study of rates of flow and of change, opened the 
way to unlimited development. The problem of finding 
the direction of the tangent at any point of a plane 
curve, is at once solved by asking : What is the ratio 
of the flows of the two co-ordinates that define the 
curve, considered as growing quantities ? In other 
words, we differentiate. To find the area of a curve 
we have to ask the inverse question : What is the 
quantity whose rate of flow divided by the rate of 
flow of one co-ordinate gives the other co-ordinate ? 
In other words, we integrate. The youth of twenty-two 
had not only solved one of the problems of the ages : 
he could give an impulse to mathematics leading to 
centuries of novel progress and growth. The differen- 
tial and integral calculus, the theory of differential 
equations, and the vast ramifications of applications 
and developments, might have been traced to the 
genius of the barely graduated scholar of Trinity. 

If Newton's discovery did not immediately set free 
the developments that we can now see should have 
resulted therefrom, if the discoverer had to face the 
possibility of being denied the credit of his own origin- 
ality, he had himself to blame. Be it out of modesty, 
or out of a sense of extreme cautiousness, Newton kept 
the discovery to himself, and denied to the world of 
science what was its obvious due, namely, a published 
statement of his discovery. 

[Newton wrote brief accounts of the method of 
fluxions as early as May and November, 1665. He 
developed it further in a manuscript dated May 16, 
1666, and still further in a tract which he wrote in 
October, 1666. . "1$ the last he made twelve applications 
of the method, to curvature, concavity and convexity, 
maxima and minimq^etc., many of the applications 
being new and of importance.^} But the plague raged 


on, Newton worked on and invented the conception 
of second fluxions, or what we now call repeated 
differentiation, and even his closest mathematical 
friends knew nothing of the great events taking place 
in this obscure youth's brain. 


Sir Isaac Newton was the boy 

That climbed the apple tree, sir ; 
He then fell down and broke his crown, 
And lost his gravity, sir. 

J. A. SIDEY : " The Irish Schoolmaster " 

THE Great Plague and Newton's enforced 
absence from Cambridge meant a serious break, 
or succession of breaks, in his work. His 
attention had already been directed towards optical 
problems, and he was preparing to undertake suitable 
experiments for the purpose of elucidating some of the 
puzzling things about light and colour, when he had 
to give up the work and retire into the country. He 
made up for this by special devotion to the pure 
mathematical studies : yet Newton's mind was essen- 
tially practical and experimental, and subconsciously 
searched for natural phenomena and their explana- 

Enforced idleness is not always a curse to the deep 
thinker, such mental leisure and freedom from immedi- 
ate preoccupation with some definite task, are a positive 
advantage. The man of science, indeed, often performs 
his function most effectively just when, to the unsus- 
pecting observer, he is enjoying a mental holiday. The 
reception of impressions and their undisturbed incor- 
poration in the mental equipment of the scientific 
worker finally give rise to the idea that, like the 



prince's kiss, removes the charm that hinders progress, 
and substitutes for it a vigorous vitality. 

Removed from his college rooms with their prepara- 
tions for optical experiments, deprived of the solace 
of mathematical treatises which only a college library 
could supply, Newton was forced to spend much of 
his exile in quiet observation of things round him, in 
meditation on problems that occupied the attention 
of his generation. The most insistent problem, one 
which demanded a solution and which was obviously 
ripe for the application to it of some outstanding 
intellect, was that of gravitation. 

When man emerged from the childlike state in which 
things were taken to be what they seemed, he was 
forced to the conclusion that the earth upon which he 
lived was not the bottom of a sort of pie-dish, with 
the sky as a cover. Little by little it was realized that 
the earth must be disconnected all round, and in the 
last few centuries B.C., and in the first few centuries 
A.D., the spherical shape of the earth became the 
accepted view of all thinkers. The heavenly bodies, 
consisting of the sun and moon and the small specks 
of light loosely called stars, were seen to move. The 
sun and moon were found to move from east to west 
across the sky each day, but the path described varied 
from day to day during the year and month respect- 
ively, in a more or less regular and periodic manner. 
Of the stars, which all appeared to move across the 
sky from east to west each night, all, except a few, 
moved regularly in exactly the same paths night after 
night, although the times of rising and setting of any 
particular star varied regularly from night to night. 
It was soon observed that this corresponded with the 
motion of the sun. The resulting view adopted was 
therefore that the heavens as a whole rotate round the 
earth from east to west each " day," this day being 
called sidereal or stellar. The sun and moon were 


assigned additional motions round the earth from west 
to east, the sun going round once in a year, the moon 
once in a month. 

But there were exceptional stars, to which the name 
planets was given. These were unlike the sun and moon 
in that they appeared on the sky as tiny specks, but they 
imitated the sun and moon in that they had additional 
motions round the earth. These planets were Mercury, 
Venus, Mars, Jupiter and Saturn. The last three, 
namely, Mars, Jupiter and Saturn, went round the 
earth from west to east on the whole in periods of 
about 2, 12 and 30 years respectively : but com- 
plications existed in the form of annual loopings, the 
planet stopping in its west to east motion, then actually 
moving back, i.e. east to west, then stopping again 
and resuming its west to east motion. Mercury and 
Venus executed motions that were at first not at all 
clear to visualize. They seemed to hug the sun in a 
peculiar manner, appearing sometimes to the east of 
the sun as evening stars, then becoming invisible and 
reappearing on the west of the sun as morning stars, 
and so on indefinitely. It was finally accepted that 
Mercury and Venus also go round the earth, but unlike 
the other or outer planets, they both take a year to 
go round the earth, and execute loops in other and 
shorter periods, 88 days per period in the case of 
Mercury, 225 days per period in the case of Venus. 

There thus arose the famous Ptolemaic system of 
the universe in which the earth was taken as spherical 
and absolutely fixed at the centre of the universe, the 
whole universe rotating round the earth once a day, 
and the moon, Mercury, Venus, the sun, Mars, Jupiter 
and Saturn going round the earth once each month, 
year, year, year, 2 years, 12 years, 30 years respectively, 
with no loop in the moon's motion, an 88-day loop in 
Mercury's motion, a 225-day loop in the motion of Venus, 
no loop in the sun's motion, and annual loops in the 


motions of Mars, Jupiter and Saturn. The circuit and 
loop were in each case represented as mption on a 
deferent and epicycle, the planet moving on the 
circumference of the epicycle whose centre moved on 
the circumference of the deferent. 

The Ptolemaic system, first given to the world in 
the second century A.D., soon became accepted doctrine. 
When European nations sank into semi-barbarism at 
least, as far as the arts and sciences were concerned 
in the early Middle Ages, the Arabs and the Jews kept 
the Ptolemaic astronomy alive, just as they kept other 
products of Greek science alive, and even made some 
significant additions. Such additions were essential 
since, after all, the only test that can be applied to a 
scientific theory is comparison with fact. If in political 
controversy facts are not seldom modified so as to 
make them fit more comfortably into some particular 
theory, it is nevertheless true that in science facts 
are supreme. A theory is indeed a summing up of a 
number of facts. If I say that two volumes of hyd'rb- 
gen explode with one volume of oxygen to produce 
two volumes of water vapour at the same temperature 
and pressure, then I do not mean that some tribunal 
has decreed that hydrogen and oxygen must do this 
and refuse at their peril. What I mean is that when- 
ever the experiment has been tried it has been found 
to yield this result. We therefore, with that faith in 
the reasonableness of nature which we call causality, 
assume perhaps with pathetic if unconscious humour 
in the eyes of a superior intelligence that the same 
result obtains in all cases, even when not observed by 
us, and will obtain in future. This is a theory about 
water. Let but one case arise in which this result is not 
obtained, and the theory begins to wobble, and unless 
the deviation from theory is adequately accounted for, 
the theory must give way to a more adequate one. 

Ptolemy's theory was not only qualitative, it had 


to be quantitative too. With their marvellous 
sense foitphilosophic values the ancient Greeks realized 
that a theory must be quantitative, that it is not 
sufficient to assert vaguely that the moon goes 
round the earth, but we must state exactly what the 
path is and how fast the motion is at any moment. 
Now the Greeks knew practically nothing about the 
science of dynamics (the other contemporary nations 
knew next to nothing of anything). There are several 
reasons why this should have been the case, as we 
shall soon see. The Greeks therefore had to make 
some basic assumptions, which we now know to have 
been without justification. They divided matter into 
earthly and celestial. Earthly matter was subjected 
to the earth's influence and moved up and down, 
perpendicular to the earth's surface. Heavenly matter, 
on the other hand, was free of this materialistic 
influence, and so moved in a perfect manner, i.e. on 
circles round the earth with constant speeds along 
the circles. 

To our modern ears such statements sound bizarre. 
Why should uniform motion on the circumference of 
a circle be the perfection of motion ? Why should 
some matter be called celestial and granted the privi- 
lege of this perfect motion ? The foundations of 
dynamics have been changed since then, and Newton 
had a great share in producing the change. Yet it 
must be remembered that even to-day there is in at 
least some of us a lurking belief that the heavenly 
bodies are somehow heavenly, while matter on our 
earth is after all only earthly. People still exist who 
dub as materialistic the astronomy that considers all 
matter in the universe as of the same kind as the 
matter of and on our earth, in spite of the fact that 
the unique position of the earth in the economy of the 
universe is no longer believed in even by such muddled 


According to the Ptolemaic system then, all the 
heavenly bodies moved on circles with uniform motions. 
The so-called fixed stars called for no further comment. 
In the case of the planets Mercury, Venus, Mars, 
Jupiter and Saturn, deferents and epicycles had to be 
introduced, but the centre of the epicycle moved 
uniformly round the deferent and the planet moved 
uniformly on the epicycle. For the sun and moon no 
epicycles seemed necessary. 

But the facts began to be troublesome. When the 
position of a planet at any moment was calculated 
from this theory and compared with the observed 
position in the sky, the agreement was often bad, in 
fact very bad, and this applied to the sun and moon 
too. Modifications had to be introduced. The centre 
of the sun's annual path was taken to be different 
from the centre of the earth, and when this did not 
suffice the uniform motion of the sun on its circle was 
taken with reference to angular motion as seen from 
some third point. And so on : in the case of each 
body such and similar complications were introduced. 
And all through the Middle Ages these complications 
accumulated. The instinct that underlay this process 
was excellent fact is supreme and theory must be 
modified to suit the facts. But clearly something was 
wrong somewhere. For there is another instinct in us 
which sees beauty and truth in simplicity, and when 
a scientific king scoffed at the astronomers by saying 
that had he been present at creation he could have 
given some good advice, he was merely giving expres- 
sion to the healthy desire of science to arrive at simple 
truth which needs no frills and furbelows to make her 

Views other than Ptolemy's had been expressed in 
ancient times, and suggestions had been made that 
possibly things are quite different. Must we assume 
the earth to be fixed, and at the centre of the universe ? 


Perhaps the earth rotates. Perhaps the earth's centre 
moves. Perhaps the earth is a body moving round 
another body, and perhaps this other body is the sun. 
Such views were, however, effectively silenced, parti- 
cularly during the later Middle Ages, when Ptolemaic 
astronomy finally conquered Europe, and became 
invested with supreme authority. Authority was the 
keynote of those days. Truth existed somewhere, and 
the search for truth meant the search for hidden 
meanings in the pronouncements of authority, be it in 
the Bible, in Aristotle, or in any other accepted and 
unquestionable source. 

A spherical earth was indeed sufficient departure from 
primitive and naive belief. To envisage humanity as 
standing all round a globe with heads pointing out- 
wards in all directions already did violence to a 
psychology that saw a physical and intellectual 
anchorage in a flat and stably-fixed earth. To deny 
the fixity of the earth and to make it wander about 
in space while gyrating on its axis meant deranging 
still further the mental equilibrium of humanity. 

New ideas were not welcomed in those days. The 
initiation of a scientific revolution nowadays meets 
with wide approval revolution is often met with open 
arms for its own sake, and accorded a publicity worthy 
of better causes. But in the later Middle Ages scientific 
originality brought with it a publicity of an undesirable 
kind and notoriety of an unpleasant character. We 
can therefore appreciate all the more the intellectual 
compulsion that forced Nicolas Copernicus to discard 
at least a part of the Ptolemaic system. 

Everything pointed in the direction of change. If 
the sun is one of the planets going round the earth, 
why should the epicycle periods in the case of Mars, 
Jupiter and Saturn, and the deferent periods in the 
case of Mercury and Venus, be exactly the same as the 
period of the sun's motion round the earth, namely, a 


year ? Why are the sun and moon exceptional in not 
having loops in their paths ? The planets are very 
far away from us : the nearest to us, the moon, has a 
distance from us sixty times as great as the earth's 
radius (it is true that in Copernicus' time the moon's 
distance was taken to be somewhat less, but this does 
not diminish the force of the argument) ; the sun is still 
further from us, the planets are still more distant, and 
the fixed stars are even further off. Does all this 
universe (and Copernicus did not, in fact, have any 
adequate idea of how vast the universe really is) re- 
volve round the earth, and as fast as once in a day of 
twenty-four hours ? 

We cannot believe direct and untutored visual 
impressions. We must use our brains and reason out 
sensible conclusions. Things are not what they seem. 
Our impressions of motion are relative : the man on 
the clift sees the ship depart from the shore, while the 
man on board the ship sees the shore and cliff depart 
from him. Copernicus was forced to the grand 
conclusion that the earth is not fixed and is not at 
the centre of the universe. The earth rotates on her 
axis once a day : this explains in rational manner the 
apparent rotation of the whole universe round the 
earth every day. The earth revolves round the sun 
once a year : this explains in rational manner the 
loops in the paths of Mars, Jupiter and Saturn, which 
also go round the sun in circles greater than the earth's 
orbit, and the peculiar hugging of the sun by Mercury 
and Venus, which go round the sun in circles smaller 
than the earth's orbit. The marvel of the exact year 
period of the epicyclic motion in the case of the outer 
planets, and the exact year period of the deferent 
motion in the case of the inner planets, now dis- 

A beautifully simple solar system emerges, slim 
in conception and unencumbered by deferent and 


epicycle. The sun is exceptional and has no looping 
motion, because it is indeed the exceptional member 
of the system, the monarch reigqing at its centre, the 
hub of the universe : the moon Has no looping motion, 
because it is also exceptional it is not a planet at all. 
The moon is a satellite, attached and subservient to 
the earth, going round the earth and playing only a 
secondary role in the solar system the Copernican 

Public attention was drawn to this view only after 
the death of Copernicus in 1543. A howl of indignation 
went up from established authority, but Copernicus 
was fortunate in being dead, for all that could be done 
to him was to execrate his name and forbid the reading 
of his book and the dissemination of his .system. It is 
generally believed that the Catholic church was mainly 
responsible for this. It is not so : all constituted 
authority, Catholic and Protestant, religious and 
secular, opposed the new astronomy. The opposition, 
in fact, was the slothful indignation of human intellec- 
tual inertia, that refused to be moved from its moorings, 
and that feared to give up the fixed earth and wander 
about with bearings lost in a bewildering universe. 
Why, even the very week was in danger : for were not 
the seven days of the week, sanctified by Biblical 
command, associated with the seven planets of pre- 
Ptolemaic astronomy ? 

Yet Qopernicus triumphed. After Galileo's dis- 
covery of the satellites of Jupiter, the phases of Venus, 
the discs of Mars, Jupiter and Saturn, no other view 
than that of Copernicus could survive. By the middle 
of the seventeenth century no enlightened person who 
was free from papal and other backward religious 
authority could do other than accept the Copernican 

It is the irony of human progress that the revolu- 
tionary very soon finds himself outdistanced by his 


disciples. Copernicus' system was a tremendous 
advance on the old system, but his dynamical know- 
ledge was hardly, if at all, in advance of Ptolemy's. 
In abolishing the central position and fixity of the 
earth, Copernicus paved the way for the abolition of 
Greek ideas of motion based upon earthly and celestial 
types of matter, and caused the emergence of the 
problem of dynamics the why and the wherefore of 
motion and changes of motion with peculiar insistence. 
But he could not liberate himself from the perfect, i.e. 
uniform circular, motions of the planets, including the 
earth, round the sun, and of the moon round the earth. 
In Copernicus' great work, " De Revolutionibus 
Orbium Coelestium" (1543), epicycles and excentrics 
are still piled upon one another : one marvels, in fact, 
at Copernicus' genius all the more in that he did 
manage to convert the earth into a rotating planet 
revolving round the sun, while he was himself yet 
subjected to the bondage of Greek dynamics, and had 
to use epicycles for other purposes. 

John Kepler was the man who actually liberated 
himself and mankind from the effects of Greek dyna- 
mical ideas in relation to astronomy ; he took the step 
that was necessary to complete Copernicus' work. 
Basing himself on the careful observations of Mars 
made by his teacher, Tycho Brahe the greatest 
instrumentalist and observer of the Middle Ages and 
also by himself, he discovered the true paths of the 

Kepler realized at the outset of his work that circular 
motions had to go. He searched for the true paths of 
the planets. He had no clue except the rather doubtful 
one that somehow the ancient Greeks had, for purely 
theoretical reasons, studied with considerable care the 
curves known as conic sections, the curves obtained 
when a circular cone is cut by a plane. This study 
had been part of mathematical education even since, 


and Kepler thought of trying whether the paths of 
Mars and the earth round the sun could be taken to 
be conies and give results in accordance with Tycho 
Brahe's observations. The conies had to be closed, 
i.e. ellipses. It was a sheer guess, the leap forward of 
the man of pre-eminent genius. 

If the earth and Mars go round the sun in ellipses, 
what is the relation of each ellipse to the sun ? An 
ellipse has three pre-eminent points inside it the 
centre and the two foci : the latter are the points used 
for drawing an ellipse quickly, since, if a string lies on 
a board with its end-points fixed, and is stretched by 
means of a pencil which runs round it, then the pencil 
describes an ellipse of which the end-points of the 
string are the two foci. We may guess that if the 
path of a planet is an ellipse, then either the centre of 
the ellipse or one of its foci will be at the centre of 
the sun. Which is the correct point ? 

If we have the correct point, the next question is : 
How does the planet move round the elliptic path ? 
What is its speed at any point of the path ? If Kepler 
had possessed any true dynamical knowledge then he 
would have found out the law of this speed very easily 
he might have forestalled Newton. But dynamical 
progress came too late for him. He had to discover 
the truth by sheer heavy arithmetical calculation. It 
was a mighty task that would have been beyond the 
powers of any other man. Kepler held out. His 
calculations were to him the romantic quest for a 
celestial gift he pursued them with the ardour and 
devotion of a fanatic. He laboured for a decade, 
without even the help of the logarithmic tables that 
were then being invented and calculated by Napier 
and Briggs in Britain. He tried hypothesis after 
hypothesis finally he triumphed. He discovered the 
laws that go by his name Kepler's laws of planetary 
motion (1609) : 



I. Every planet moves on an ellipse with a focus at 
the centre of the sun ; 

II. The line joining the centre of the sun to the t 
centre of the planet sweeps out equal areas in equal 

3i A Aphelion 

FIG. 2 


Simultaneous positions of two planets in their orbits. AP/A'P* = 1*84, so that 
ratio of periodic times is i 84" /a = 2.5. Circles represent oppositions of the two 
planets. Squares represent conjunctions of the two planets. 

The first law is intelligible, but what does the second 
law mean ? Kepler did not know. He was the 
discoverer of the truth but not of the significance of 
this truth. It was a great achievement to discover 
the true paths of the planets. It was the coping-stone 
to the Copernican system, the completion of the 


revolution initiated by Copernicus, which did away 
once and for all with the deferents and epicycles, 
excentrics and equants of mediaeval astronomy. 
Kepler put into the Copernican system the spirit of 
modernity. How Copernicus would have rejoiced to 
learn the truth from his posthumous disciple ! 

Kepler had yet another problem to solve the 
problem of his youth. Was there any relationship 
between the distances of the planets from the sun ? 
He had foolish speculations at first, but he finally hit 
upon a wonderful and simple truth. His third law 
(1619) : 

III. The square of the time taken by a planet to 
describe its path completely once round the sun is 
proportional to the cube of its mean distance from 
the sun 

is indeed a peculiar law, savouring of the mysterious 
that Kepler loved so well. 

A new problem now began to emerge. Whereas the 
question so far had been : How do the planets move ? 
the question now became : Why do the planets move 
in the manner discovered by Copernicus and Kepler ? 
The motions of the planets had been found : they had 
to be explained. This became particularly urgent 
when Kepler published his laws. One might perhaps 
ascribe uniform circular motion to celestial matter and 
flatter oneself that one is doing something sensible 
but it becomes difficult to do this conscientiously with 
elliptic motion round a focus in which the " radius 
vector " sweeps out areas proportional to the time. 
Planets may be deities and as such choose to march 
sedately and majestically in perfect circles with 
unvarying speeds impervious to all influences tend- 
ing to hurry or to delay them. But it is difficult to 
envisage a planetary deity at the end of a sort of 
municipal rolling broom, that obeys trade-union rules 


and sweeps out so much area per day no more and 
no less. 

Kepler himself tried to explain the motions that he 
had unravelled. He failed. A sort of gravitational 
influence of the sun on the planets was suggested by 
him, even the law of the inverse square of the distance 
suggested itself to him and to others in France, in 
Italy and in England but to no effect. A dynamical 
explanation of planetary motions was out of the 
question so long as the foundations of dynamics had 
not been discovered. 

It is for this reason that the Vortex Theory of Descartes 
enjoyed such a vogue. To explain with considerable 
plausibility the whirling of the planets round the sun, 
and of the satellites round the planets, one need only 
observe the way in which whirlpools in water carry 
with them the bodies caught by them, forming minor 
whirlpools or eddies, which exert local influences of 
the same kind. Descartes therefore postulated vortices 
in an ocean of " ether," filling up the whole of the 
space occupied by the solar system. 

Quantitatively, Descartes' theory breaks down, but 
it held the field because there was no competitor. 
Vague ideas about gravitation could not dethrone a 
theory supported by the authority of this great 
philosopher and mathematician. Views based upon 
sound dynamical principles alone could rout the vortex 

Fortunately, the dynamical principles were soon 
available. Galileo's great astronomical discoveries 
have had the effect of eclipsing somewhat the lustre 
of his fame in the history of dynamics. If astronomy 
suffered from the arrogance of self-constituted authority, 
it had at least one advantage observation of the skies 
was encouraged both by nature and by man. A man 
is indeed no higher than the beasts of the field if he 
is not attracted by the aspect of the heavens, especially 


in the clear skies of Italy. The observation of the 
heavens was also encouraged (from mixed motives) by 
kings and princes. When man believed that the 
heavenly bodies shone for his benefit and so as to 
enable him to foretell the future of his petty affairs, 
detailed study of these bodies was an essential consti- 
tuent of government and statesmanship. The emperor 
Rudolf may have meant astrology when he installed 
Tycho Brahe in Prag Tycho Brahe could get on with 
his astronomy nevertheless. Astronomical discovery 
was thus in a sense inevitable. In the case of dynamics, 
however, if nature did occasionally suggest feebly : 
" Observe the motions of bodies and the causes of 
these motions," man did not respond to the invitation. 
Why observe the motions of bodies when Aristotle 
has told us all about them already ? This would 
only tend to encourage scepticism and to undermine 

And dynamical laws required very exceptional 
powers of observation and of intuition for their 
unravelling. It is difficult nowadays to measure 
accurately the velocity with which a body is moving 
at any moment in the early seventeenth century it 
was quite impossible. It was even difficult to observe 
accurately the position of a falling body from second 
to second, in an age when the measurement of time 
did not yet enjoy the help of modern clocks and 
chronographs. Further, motions are liable to all kinds 
of disturbances air resistance, friction, surface irregu- 
larities, and so on. Finally, where was the mathe- 
matical machinery for dealing with motions and 
changes of motion before Newton invented it in his 
method of fluxions ? 

It was Galileo who ventured to dispute the authority 
of Aristotle in the dynamical field. He experimented 
and he discovered that the rate of fall of a body near 
the earth does not depend upon the weight of the 


body if this weight be sufficient in relation to the 
size of the body to make the effect of air-resistance 
negligible. Bodies falling from the same level reach 
the ground after the same interval of time. Finally 
he discovered that a falling body moves in a re- 
markable manner its speed increases with the time 
in a perfectly regular manner, it is accelerated 

The regular increase in the speed of a falling body 
is of course due to the pull of the earth on the body, 
what we call the body's weight. It must follow 
therefore that a steady pull produces a steady increase 
of velocity a new and a revolutionary idea. To the 
forerunners, and even to the contemporaries of Galileo, 
motion connoted force wherever motion existed force 
had to exist to explain it. In Galileo's mind a new 
idea began to dawn : not motion connotes force, but 
change of motion connotes force. A body moving 
under no force enjoys constant speed in constant 
direction : let a force act upon it and its speed or its 
direction or both will vary. Galileo could not prove 
this directly, since a body moving under no force 
cannot be realized. But the man of genius sees 
further than the limited range of the available experi- 
ence he makes the leap that carries the human soul 
forward on the wings of discovery, and Galileo was a 
man of exceptional genius. 

Here was the beginning of true dynamics. The 
ancient belief was no force, no motion. The modern 
view is no force, no change of motion, i.e. no accelera- 
tion. Need we wonder at the circumstance that this 
truth lay so long undiscovered ? Think of the ox-cart 
in which Homer's father went to market think of the 
hardships of locomotion in those days, and right down 
nearly to our own generation. The only smooth road 
known then was the sea and the sea gave the sea- 
farers of those days sufficient to think about to divert 


their minds from dynamical speculations. It needed 
a mighty intellectual effort of scientific abstraction to 
dissociate locomotion from the jolting and the sense 
of effort that accompanied it, and to see in the ideal 
smooth and unvarying motion the raw matter, so to 
speak, of dynamics. 

The discovery of the true laws of motion in 1637 
set the road free for progress in the dynamics of 
astronomy. Men of the greatest eminence sought for 
the solution of the problem of the planets. Robert 
Hooke in England a man of considerable, if erratic 
and unstable, genius, the discoverer of the ut tensio 
sic vis of elasticity speculated on this problem, and 
even announced that no doubt he could solve it by 
combining the conception of gravitation with the dyna- 
mics of Galileo if only he could hit upon the correct 
law of force to attribute to the sun's gravitation, the 
exact way in which this force depended upon the 
distance of a planet from the sun. It was the youthful 
Newton, meditating in the exile of his Lincolnshire 
garden, who approached the problem with a direct 
frontal attack, remarkable and historic even in its 
initial failure. 

(Tradition relates that one day in 1666 Newton was 
sitting in his garden at Woolsthorpe, when he saw an 
apple fall from a tree : this suggested gravitation to 
him, that the fall of the apple was due to the earth's 
pull, and hence arose his discovery of the law of gravi- 
tation] There is a rival tradition which makes Newton 
observe the fall of the apple through a window on the 
first floor of the manor house. The apple tree itself 
became the object of general interest and historic sig- 
nificance, and it was kept standing till blown down by 
a gale in 1820. A chair made from the wood of this tree 
is to be seen at Stoke Rochford. Descendants of the 
tree are said to be thriving to this day ; but all efforts 
to make the descendants take root in their original 


and ancestral garden at Woolsthorpe have met with 
no success ! 

Popular imagination clings to this apple incident 
yet j it is clear that Newton was not the first man ta 
see an apple fall, or to ask himself why an apple falls. 
Newton did not discover that the earth pulls the apple 
the earth's gravitation was common knowledge in 
ancient times, and Galileo had, when Newton was still 
unborn, discovered all about the fall of an apple or 
of any other body free to give way to the earth's pull. 
The fall of the apple if it was really responsible for 
initiating in Newton's mind the train of thought that 
culminated in the discovery of the law of gravitation 
did it in the following manner, if one may venture 
to put into feeble words the flash of Newton's genius : 

" Why do the planets go round the sun ? Why do 
they not move in straight lines ? Evidently there is 
a force pulling them out of the straight-line path at 
every moment, and clearly this force is due to the sun. 
The moon goes round the earth and does not go off in 
a straight line. This must be due to the earth. Ah ! 
An apple has just fallen to the ground : the earth has 
pulled it down. How far up does the earth's influence 
extend ? We know that no matter how high up we 
go to the summits of the highest mountains this 
influence exists without obvious weakening. Does the 
earth's gravitation extend to any distance, no matter 
how great perhaps even as far as the moon ? Can > 
this be the force that compels the moon to accompany/ 
the earth, to travel round and round the earth indefi-l 
nitely as the earth travels round the sun ? \ 

" Yes, this is a pretty theory : can it be proved ? 
Can it be shown that the pull required to explain the 
moon's motion is just that afforded by the earth's 
gravitation ? Any attempt at such proof must postu- 
late some law according to which the gravitative pull 
of the earth varies with the distance from the earth ; 


for clearly we cannot suppose this pull to be the same 
for all distances, even to the ends of the universe. It 
must diminish as the distance increases. What is the 
law of this diminution ? Suppose that one body is 
twice as far from the earth's centre as another : what 
is the relationship between the pulls exerted by the 
earth on these bodies ? " 

The most important step in the solution of any 
natural problem is the formulation of the problem itself. 
Newton formulated his problem in masterly manner 
it only remained to attack the solution. Two steps 
had to be taken. The first was to determine how a 
gravitational pull would vary with distance from the 
gravitating body. The second was to see whether the 
earth's pull on the falling apple could also account for 
the motion of the moon. 

How should a gravitational pull vary with distance ? 
A very simple consideration at once suggests a solution. 
Suppose that from a point O there is a gravitational 
influence in all directions. Take two spheres with 
centres at O, one having double the radius of the other. 
The same gravitational influence is spread out over 
the surfaces of the two spheres : but the sphere of 
double radius has a surface area four times that of the 
smaller sphere. It follows that the gravitational pull 
at a point on the larger, double, sphere must be one- 
quarter of the pull at a point on the smaller sphere. 
This is at once generalized into the inverse square law, 
namely, that the pull exerted at any point is inversely 
proportional to the square of the distance of this point 
from the gravitating body. 

Such considerations would run through Newton's 
mind ; but Newton was remarkably realistic in his 
outlook upon nature and her problems. An ounce of 
observational or experimental proof was worth to 
him more than a pound of theoretical argumentation. 
This characteristic accompanied him all through his 


long career of scientific activity. Newton looked for 
observational justification of the inverse square law 
and the third law of Kepler, discovered nearly half a 
century before, and quite ununderstood all that time, 
gave him the proof he desired. 

The planets move on ellipses : but these ellipses are 
nearly circles this was indeed why circular motions 
were insisted upon till Kepler's success in emancipating 
us from them. Except for the planet Mercury, the 
planetary paths are so nearly circles that, for a rough 
calculation, we can ignore their ellipticities and assume 
them to be circles with their centres at the centre of 
the sun. Further, the motions on the paths are variable 
yet the variations are really very small and we can 
for a first approximation imagine the planets to describe 
circular paths with constant speeds. 

It needed the mental courage of a Newton to thrust 
himself back in this way into the primitive views of 
Greek astronomy uniform circular motions. Newton 
was not yet mathematically ripe to solve the problem 
of the planets in their fullness. With characteristic 
clarity of vision he pounced upon the essential and 
discarded the inessential. He felt that what he needed 
could be obtained by such approximate argumenta- 

Now if a body moves on a circle with constant 
speed there must be a force producing the continuous 
change in direction of the motion ; this follows from 
Galileo's dynamical discoveries. Every schooboy who 
has done a little mechanics knows that the force 
required is the mass of the moving body multiplied by 
the product of the speed into the rate at which the 
direction of motion is rotating. This means that for 
radius r and angular velocity n the force per unit mass 
of the moving body must be the speed rn into the rate 
at which the direction of motion rotates, namely, n. 
Hence the force per unit mass must be n*r. 


But Kepler's third law states that the squares of 
times taken by the planets to travel once round the 
sun vary as the cubes of their mean distances fr. >m the 
sun. If then T is the time for a planet moving in a 
circle of radius r we get T 2 proportional to r*. l>ut 
the time of a complete revolution varies inversely as 
the angular velocity n, since the time multiplied by 

n r (velocity) 


FIG. 3 

If body moves with constant angular \<>1 >city n in of radius r, acceleration 
ib n*r towards the CL-ntte. 

the angular velocity must give the complete angle all 
round, or four right angles, i.e. the same for all the 
planets. Hence n 2 is proportional to i/r 3 so that n*r 
is proportional to i/r 2 . This is of course the inverse 
square law ! 

Newton then argued by analogy that if the gravita- 
tional pull of the sun on the planets follows the inverse 
square law, then the pull of the earth on the apple and 
on the moon must also follow the inverse square 
law. Why ? Because Newton had a profound lx lief 
in the unity of the universe, in the similarity of effects 
produced by similar causes that truth is independent 
not only of time but also of place, so long as at difknent 
times or at different places we look for the results 


produced by exactly similar causes. If the motion of 
the moon is to be explained by the earth's gravitation 
then it can only happen on the basis of the inverse 
square law. 

The distance of the moon from the earth's centre is 
about sixty times the radius of the earth itself. It 
follows therefore that the gravitational effect of the 
earth on a unit mass of the moon must be one part in 
3,600 of the effect produced on a unit of mass near 
the earth's surface, say, a falling apple. The accelera- 
tive effect on the moon must therefore be 1/3,600 of 
the accelerative effect oh the apple. The accelerative 
effect on the apple is to add a speed of 32*2 feet per 
second each second. Hence the accelerative effect on 
the moon must be a speed of 32-2/3,600 feet per second 
added each second, i.e. 0*00895 feet per second added 
each second. 

Is this accelerative effect equal to n 2 r, where r is 
the radius of the moon's path in feet and n is the 
angular velocity of the moon round the earth in true 
mathematical measure, i.e. in radians * per second ? 
We know r to be 6oR where R is the earth's radius 
in feet. As regards n we know that the moon 
describes 360 round the earth in about 27 \ days : this 
makes n equal to 1/375,000, with the result that the 
acceleration produced by the earth's pull on the moon 
is -R/2,344 f ooo,ooo where R is the earth's radius in feet. 

Everything depends upon R, the radius of the earth. 
This is a very difficult quantity to measure, but Newton 
lived at a time when accurate knowledge of the size of 
the earth had already been obtained. Yet he was far 
removed from books and he had to rely on memory. 
It was commonly supposed that the size of the earth 
is such that a degree of latitude is 60 English miles. 
Newton adopted this view and made the complete 

* A radian is the angle subtended at the centre of a circle by an 
arc of the circumference of length equal to one radius. 


circumference 360 times this, or 21,600 miles. The 
radius was therefore 3,440 miles or about 18,160,000 
feet. The acceleration of the moon should thus be 
0-00775 feet per second added each second. 

Galileo gives 0-00775, Kepler gives 0-00895. The 
latter exceeds the former by nearly sixteen per cent ! 

" This is not equality," said Newton to himself. " My 
thought has been but an idle speculation. This great 
problem is not to be solved by me. Yes, I can patch 
up my theory and imagine all kinds of causes to 
account for the apparent deficiency in the moon's 
angular motion. But I can only deal with realities, 
with forces which I know something about. To 
postulate mysterious agencies whose effects I cannot 
measure directly is not a useful contribution to the 

We must pause and observe this young man, 
twenty-three years of age. By sheer genius he has hit 
upon the very secret of the heavens, and carried out 
calculations in which lie the germ of the complete ex- 
planation of the motions of the planets. Yet Newton 
does not dare to conclude that his theory is right, because 
there is a discrepancy of sixteen per cent in the quan- 
titative investigation. The leap of genius must not 
be confounded with intellectual recklessness. The dis- 
coverer must be true to himself. His ego is indeed an 
invaluable ingredient of his work but it must be the 
ego of honest personality, not that of selfish egotism. 
We can picture the pang with which Newton abandoned 
his theory, how his innate intellectual honesty struggled 
with human weakness in his closet on the first floor 
of the Woolsthorpe manor house the tiny room that 
can still be visited and admired as the hallowed shrine 
of the true spirit of discovery and conquered. If 
ever the scientific method scored a victory it was in 
the humble home of the widow and her orphaned 


Not a word did Newton say of all this to a living 
soul. He had failed and there the matter ended. It 
did not really end there, for about sixteen years later 
New tun discovered the source of the discrepancy and 
the cause of his failure the simple fact that the value 
of R he had assumed was too small, and that he should 
ha\e taken it by about fifteen per cent greater ! 
Perhaps humanity is all the better for the apparent 
failure and the delay in the ultimate success. Is not 
this example of intellectual honesty and of impersonal 
devotion to the cause of scientific truth as valuable 
as any contribution to human spiritual values ever 
made by mortal man ? 


Behold, a prism within his hands 

Absorbed in thought great Newton stands, . . 

The chambers of the sun explored, 

Where tints of thousand hues were stored. 

^ ^HE Great Plague was responsible for interrupting 
I an experimental investigation which turned out 
^ to be Newton's main work for a decade. The 
discovery of the telescope and its remarkable use at 
the hands of Galileo naturally made optics in general, 
and telescopes in particular, the subject of keen interest 
on the part of all the scientific men of the seventeenth 
century. Newton's attention was drawn to the subject 
in a very natural manner. He himself records that 
early in 1664, when he was still an undergraduate, he 
observed and measured lunar crowns and halos. 
What Newton did in optical research during the next 
two years we cannot say, but we do know that in the 
beginning of 1666 he bought a prism to examine the 
phemonena of colours. He tells us himself that 
having discovered why the telescopes of those days 
were defective, he was led to consider the making of 
telescopes based upon reflection. " Amidst these 
thoughts I was forced from Cambridge by the Inter- 
vening Plague, and it was more than two years before 
I proceeded further." Newton did in fact proceed to 
construct a reflecting telescope till late in 1668. It 
is therefore clear that the first notions of Newton's 
great discovery of the spectrum must have come to 



him in 1666. We know that he was absent from 
Cambridge in 1666 up to about the end of March, and 
then from about the beginning of July onwards till 
the end of the year ; hence it is highly probable that 
Newton's first glimpses into the true nature of colour 
were obtained early in 1666, and that he made some 
experiments between April and June of that year. 
Newton was then twenty-three and a half years of age. 

A telescope is based upon the following fundamental 
idea. An image of a distant object is formed by means 
of a lens called the object glass and this image is 
then observed by means of another lens called the 
eye-piece. The construction of the most complicated 
modern telescopes is based upon essentially the same 
idea. It therefore seems to be an indispensable con- 
dition of a good telescope to make the object glass 
collect the rays from any point of the object observed 
accurately to a focus. If rays from any point of the 
object do not give an exact point image, then the 
telescope suffers from aberration and its optical value 
is diminished the picture in the telescope is indis- 
tinct, which is bad for the eyesight and bad for exact 

It is, however, a remarkable fact that the only form 
of optical operation that brings rays emanating from 
a point to an accurate and exact focus at another 
point is reflection at a plane surface. The perfectly 
plane mirror gives a reflection which is perfect in 
sharpness of outline and of detail. Any other optical 
operation, especiaDy refraction or light bending at a 
plane or any other surface between one medium, say 
air, and another, say glass, gives more or less blurring 
and indistinctness. 

This fact was soon understood and the problem of 
optics narrowed down. If it is impossible to get 
an exact image of all points of the object, it may 
yet be possible to secure an exact image of one point 


of the object for scientific, especially astronomical, 
purposes this would be a great thing, nearly as much 
as is really needed for useful work. 

Even this modest demand is not easily satisfied 
in an ordinary telescope arrangement, in fact is quite 

FIG. 4 


Rays OP lt OP,, OP,, etc., from the point O, are bent into the directions P^,, 
PQ, PtQa, etc., when passing from air into glass ; these new directions are not 
concurrent ; hence " spherical abenation." 

out of the question if the surfaces of the object lens 
are plane or spherical. Thus if P^Pa represent 
a plane surface of separation between air and glass, 
and OPj, OP 2 , OP 3 , ... are rays from a point O 
striking the surface at P t , P a , P 8 . . ., then the new 


rays after refraction, namely, l^Qi, P 2 Qa> PsQs - 
do not pass through one point they form in fact a 
very complicated bundle of rays which do not give a 
sharp image point at all. The same applies to 
refraction as this is called at a spherical surface 
of separation between air and glass. How is this 
difficulty to be overcome ? 

This " spherical aberration " engaged the attention 
of the mathematicians of the generation immediately 
preceding Newton. When Galileo first invented and 
used his telescopes he added to astronomical science an 
instrument of marvellous power but the telescopes he 
used were nevertheless very defective instruments, 
and no doubt Galileo's blindness towards the end of his 
life can be traced to the strain he imposed on his 
eyesight in using these telescopes so assiduously. 
The cause was taken to be the spherical aberration 
just indicated, and search was made for a means of 
eliminating it. 

It was the great Descartes who suggested what 
appeared to btf a really good way out of the difficulty. 
He looked at the problem in a somewhat different way. 
Instead of assuming that lenses must have plane or 
spherical surfaces he asked himself the following 
question : " Given an object point O, rays from which 
are to be refracted at some surface of separation 
between air and glass, so as to pass through another 
and image point I, what should be the form of surface 
used ? " Only in one case can a spherical surface be 
used, and this is of no value for telescopic purposes 
it is really of fundamental importance for high-power 
microscopic objectives as constructed nowadays. 
Descartes found that to get the surface he wanted he 
had to depart from the spherical shape, and grind the 
lenses in accordance with new curves that beai his 
name Cartesian ovals : he therefore suggested the 
use of these new surfaces, and even devoted time and 


energy to the devising of machines for producing such 
surfaces on glass. 

Yet it was all a fallacy. In actual fact the grinding 
and polishing of non-spherical surfaces on glass is on 
the whole impracticable, and spherical surfaces are 
the basis of applied optics to this day. But even if 
perfectly ground and polished surfaces of exactly the 
form indicated by Descartes' theory could have been 
produced, they would have yielded practically no 
improvement in the optical properties of telescopes. 
It was not spherical aberration that was to blame for 
the imperfection of Galileo's telescopes. The blame 
belonged really to a cause of which Galileo, Kepler 
and Descartes were all ignorant an ignorance all the 
more striking since so many natural phenomena flow 
from the same source. 

The colours of the rainbow, with its promise of peace 
and reconciliation after the storm, the flash of the 
diamond, the colours of the prism, the charm of the 
soap-bubble, why the very things observed in the 
telescopes of the period, seemed to beg for elucidation 
by an almost obvious principle yet the principle lay 
hidden from the human understanding, and needed 
the genius of Newton to give it to the world. Already 
in 1666, when twenty-three years of age, Newton had 
decided to experiment with the prism, and had reached 
the momentous and fundamental conclusion that the 
telescopes of Galileo and Kepler were incapable of 
improvement, and that a new principle of telescopic 
construction had to be employed?] 

It seems to be impossible to say how much knowledge 
of the phenomena of colour Newton had acquired when 
he reached this conclusion. He did not publish an 
account of his researches till five or six years later, and 
in this account a clear chronology is not given. We 
find moreover that when about three years later in 
1669 he helped his great teacher and friend Isaac 


Barrow in the publication of a set of lectures on optics, 
Newton did not even then correct Barrow's quite 
absurd notions about colour. We must therefore con- 
clude that Newton himself was not quite clear on the 
subject, even after he had abandoned attempts to 
improve Galileo's telescope. The fact, however, that 
Newton did reach the conclusion to discard Descartes' 
idea and to turn to reflecting telescopes instead, 
cannot but indicate that he had discovered the main 
principle underlying such conclusion. 

The fact is of course that in addition to the spherical 
aberration difficulty of which the great mathematicians 
before Newton were quite aware, there exists another 
cause of indistinctness and imperfection in refraction 
which they did not suspect, and which Newton dis- 
covered. We need not devote much space to the 
description of this discovery and the method adopted 
by Newton to make it. Every man or woman who 
claims to possess the rudiments of scientific culture 
surely knows that when a beam of parallel white light 
is sent through a prism so that it is deflected by 
refraction, it does not emerge as a beam of parallel 
white light, but rather as a bundle of beams of all 
colours no longer parallel but pointing in different 
directions. Newton sent a beam of sunlight of 
circular section through a prism, so that it was bent 
once on entry into the prism and once on emergence 
from the prism : when caught upon a screen two 
effects were observed. The screen gave a coloured 
patch of light instead of a white patch : this in itself 
was not so very unexpected, since Newton, like millions 
of intelligent human beings before him, had observed 
that prisms produce colours this is why prisms are 
so popular for purposes of adornment round lights 
and in windows. But the second effect observed was 
unexpected and thought-provoking. The original 
beam was circular in section : the patch of coloured 



light on the screen was lengthened in a direction at 
right angles to the edge of the prism ; and it was no 
moderate lengthening the patch was five times as 
long as it was broad. This was completely at variance 
with all contemporary doctrine on the passage of rays 
through prisms. 

Perhaps Newton did not at once solve the mystery 
judiciously chosen and carefully executed experi- 

White light split up into coloured rays when passing through a prism, forming 
the spectrum. 

ments were yet necessary in order to explain this 
new phenomenon, and these Newton carried out during 
the succeeding five years. But one thing was obvious 
to him. If refraction through a prism converts a thin 
circular beam of light into a beam whose section is a 
long strip, then clearly a telescope that depends upon 
refraction through a lens cannot but produce imperfect, 
coloured and blurred images. This did not depend 
upon the exact shapes of the lens surfaces. Cartesian 


ovals were simply irrelevant to the problem. A lens 
cannot produce a clear and sharp white image of a 
star colour must be introduced and cause con- 
fusion : the aberration to be eliminated was not 
spherical aberration but " chromatic " aberration, 
error due to colour. Whatever the cause of chromatic 
aberration may be, it is not produced by reflection at 
any surface, plane, spherical or of any other form, 
as Newton soon discovered. Hence came Newton's 
decision to relinquish refracting for reflecting telescopes, 
especially as three years before then, in 1663, James 
Gregory of Aberdeen had already proposed this type 
of instrument . But Gregory was in complete ignorance 
of the cause of the imperfection of refracting telescopes, 
and in any case he never made a reflecting instrument 
at all. Newton discovered the cause which had 
baffled the mightiest intellects of the generation before 
him when he was a graduate of one year's standing, 
and made a reflecting telescope with his own hands 
about two years later. 

The three subjects to which the youthful Newton 
devoted the years immediately following his graduation, 
and in which he made such remarkable discoveries so 
early in his career, were an epitome of his life's work. 
Fluxions, gravitation and optics these were the main 
concern of the whole of his scientific life. For over 
thirty years he continued to achieve conquest after 
conquest. A decade he devoted largely to the prosecu- 
tion of his optical researches and to the consolidation 
of the great discovery of the spectrum, A second decade 
he devoted to the working out and publication of his 
still greater discovery of the fact and the law of 
universal gravitation, the discovery that Newton is most 
often remembered for and in which his influence is 
still alive to-day. The subsequent decade of his 
scientific life at Cambridge Newton devoted to the 
further development of his astronomical work, and 


the consolidation of his pure mathematical researches, 
notably the method of fluxions. No other man in 
the history of science presents a record of devoted 
service in the cause of science with such conspicuous 
genius and success. 


Bright effluence of bught essence increate. 
Or hear'st thou rather, pure ethereal stream. 
Whose fountain who shall tell ? 

JOHN MILTON : " Paradise Lost," Book III 

NEWTON returned to Cambridge early in 1667* 
The latest recorded absence due to the Plague 
was Lady Day, 1667. He said nothing to any- 
body about his discoveries and ^peculations in mathe- 
matics, astronomy and optics. JHis merit was obvious, 
however, and on October i, 1607^ Newton was elected 
Minor Fellow of Trinity College^ He could now settle 
down and work without any serious economic worries, 
and devote all his attention to the sciences. 

There is reason to believe that as Fellow of Trinity 
Newton was assigned rooms in the staircase which has 
since become famous as Newton's staircase, east of 
Great Court. The rooms he occupied hen were not 
those pointed out nowadays as Newton's rooms, but 
rather the ground floor apartments abutting on the 
College Chapel. The so-called Newton's rooms, on 
the right-hand side on the first floor, were occupied by 
him later on. 

Newton was soon busy at his researches with drills 
and hammers, magnets and compasses, prisms and 
materials for polishing glass and metal. He spent a 
few months in Lincolnshire, staying there in December 
over Christmas, 1667, and into the month of February, 
1668 : but he returned to Cambridge and took the 


THE OPTICAL DECADE, 1668-1678 68 

degree of M.A. in March. He was elected Major 
Fellow in the same year. He spent August and 
September in London, no doubt for the purchase of 
materials for his optical and other, especially chemical, 
experiments, and then returned to Cambridge in order 
to execute the design of more than two years' standing, 
namely, to make a reflecting telescope. 

James Gregory had proposed a reflecting instrument 
consisting of two concave mirrors turned towards one 
another. Light from the object to be observed was 
to be reflected from one of the mirrors the wider one 
to a focus in front of the smaller mirror. The latter 
would reflect the light again and bring it to a focus 
through a hole in the first mirror so as to be observable 
by a person placing an eye-piece behind this hole. 
Newton very much disliked the hole in the larger 
mirror, and preferred instead of the second concave 
mirror a plane mirror placed at 45 with the axis of 
the telescope. The rays would thus be reflected to a 
focus through a hole in the side of the telescope tube. 
Newton's idea is the one usually followed nowadays, 
though a variant of Gregory's form, in which the small 
concave mirror is replaced by a small convex mirror 
the hole in the large mirror and eye-piece behind it 
being retained is represented by one very large 
reflector in existence to-day. This form is known as 
Cassegrain's telescope : Cassegrain was a contemporary 
of Gregory and of Newton. 

There is not really very much to choose between the 
different forms, as Newton himself admitted. New- 
ton's real merit consists in the fact that he actually 
made such an instrument the first reflector in 
history towards the end of 1668. It was not a great 
instrument either in size or in performance. Its 
aperture was one inch and its length was six inches. 
Newton used a magnification of forty times, and 
claimed that this was as much as could be done with 


a refracting telescope six feet long. He turned the 
telescope to the sky and saw with his tiny instrument 
the disc of Jupiter and the then known four satellites 
very nicely, and the phases of Venus with a little 

While Newton was working at this instrument, and 
engaging himself in researches of a chemical nature 
he spent quite considerable sums of money on chemicals, 
furnaces, and a " theatrum chemicum " in April, 
1669 the turning point in his career was close upon 
him. Isaac Barrow, a famous preacher and an 
excellent mathematician, had had Newton under 
observation for several years. Barrow was the first 
Lucasian professor of mathematics in the university, 
and had contributed with distinction to the develop- 
ment of geometry and analysis. In 1669 Barrow 
decided to devote himself entirely to theology and to 
resign the Lucasian chair. A successor was needed, 
and with remarkable vision Dr. Barrow nominated the 
twenty-six year old Newton for this post. No doubt 
Barrow was influenced to do this by two indications 
he had received of Newton's learning and ability. 
The first was Newton's help in Barrow's publication of 
his lectures on optics in 1669. The second was a 
paper that Newton gave to Barrow in the same year, 
entitled " On Analysis by Equations with an Infinite 
number of Terms," the first written statement on New- 
ton's discoveries in mathematics, particularly fluxions, 
that we know to have found its way into another man's 
hands. Newton suggested that the paper might be 
sent to John Collins, a contemporary mathematician 
who corresponded with many mathematical workers 
and acted as a sort of liaison between them. Barrow 
received the paper in June, 1669, he sent it to Collins 
on July 3ist, and three weeks later Barrow wrote 
again to Collins expressing pleasure at the favourable 
opinion that he had formed of the paper and divulging 

THE OPTICAL DECADE, 1668-1678 65 

that the author was Isaac Newton. Collins took a 
copy of this paper and returned the original. It is 
remarkable that Barrow and Collins, more experienced 
men than Newton, also failed to realize the importance 
of publishing the paper, both for Newton's own reputa- 
tion as well as for the advancement of learning. It was 
not till forty-two years later that the contents of this 
manuscript were given to the world. In this way was 
Newton's priority as the discoverer of the fluxionary 
method allowed to come under a shadow of doubt,! 
and the seeds of future unpleasantness sown. 

(jNewton's brilliance was recognized in Cambridge, and 
he was appointed Lucasian professor on October 29, 
1669^ As professor Newton had to lecture once a week 
one 'term each year on some mathematical topic, and 
to devote two hours per week to audiences with 
students who wished to consult the professor about 
their work and any difficulties they might have 
encountered. Newton chose to lecture on optics, for 
he was then in the midst of his further researches on 
the spectrum, the results of which he laid before his 
students. The lectures as such were not published 
till very long afterwards, when Newton had already 
left Cambridge and relinquished the professorship. 
Fortunately, however, his optical work was to come 
before a wider audience of scientific men in a somewhat 
peculiar manner. Later he lectured on algebra and 

Newton did not himself have a very high opinion 
of his little reflecting telescope. He made a second 
instrument, of about the same size as the first, but 
slightly better. The Royal Society, which had been 
founded at the instance of King Charles II in 1667, 
got to hear of the actual existence of a reflecting 
telescope, and sent a request to Newton that he might 
send them the instrument for inspection. It seems 
that Newton was a little vainer about his practical 


workmanship than his theoretical researches, for he 
readily acceded to this request. The instrument was 
sent to London, and not only the Royal Society, but 
also the King, saw it and expressed admiration for it. 
This telescope still exists as one of the most treasured 
relics in the possession of the Royal Society to-day. 

The reputation of the telescope maker began to 
spread. [lie was at once proposed for election to the 
Royal Society, and elected without delay on January 
II, 1672!) This compliment pleased Newton very 
much, and he promptly offered to communicate to 
the Royal Society what he considered to be far more 
important and valuable, namely, his discovery of the 
spectrum and of the nature of colour. Newton's own 
opinion of his discovery is interesting in view of his 
general modesty and soberness of expression : he refers 
to it as " being in my judgment the oddest if not 
the most considerable detection which hath hitherto 
been made into the operations of nature " I 

[On February 6, 1672, Newton sent his paper to 
Oldenburg, the Secretary of the Royal Society, and it 
was published soon afterwards. By then Newton 
had reached more definite conclusions about the 
mysterious five-fold extension of the^ section of a beam 
of light on passing through a prismT] At first Newton 
looked for various and quite impossible ways of 
explaining this result. But the conviction soon dawned 
upon him that there must be in the divergent coloured 
beam a number of beams of different colours, which 
had suffered different deviations by refraction through 
the prism. He found that the coloured patch could be 
made white again and the section restored to its 
original circular shape by taking the divergent coloured 
beam through another exactly equal prism, but with 
the bending taking place in an opposite sense to the 
refraction through the first prism. He then examined 
the light falling on various portions of the extended 

THE OPTICAL DECADE, 1668-1678 67 

patch on the screen. He was able to prove quite 
clearly and conclusively that these lights were all 
different from one another, and did actually suffer 
different refractions in going through the prism. 
Red, orange, yellow, green, blue, indigo, violet were 
the colours thus distinguished, the bending suffered 
through the prism being least for the red light, and 
increasing till the greatest bending was suffered by 
the violet light. 

This was indeed a " considerable detection . . , into 
the operations of nature." White light is not homo- 
geneous : it consists of differently coloured rays of 
varying refrangibility, or liability to be bent in passing 
from one medium into another. A convex lens will 
therefore not produce one white image, but a number of 
coloured images, a violet one nearest the lens, a red 
one furthest from the lens, and the other colours 
ranging in between. The cause of the imperfection of 
telescopes became quite obvious. 

All this Newton set out in his paper to the Royal 
Society. He justified in this way his making the 
reflecting telescopes, and suggested that reflecting 
microscopes might also be made. Let it be said at 
once that the reflecting telescope of Newton was but 
the forerunner of mighty instruments based upon his 
construction. The hundred-inch reflector at Mount 
Wilson Observatory in California is a direct descen- 
dent of Newton's tiny telescope, through a long and 
noble lineage of reflecting telescopes made by William 
Herschel. Nothing considerable ever came, however, 
of the suggested reflecting microscope. 

But Newton went further. Colour became to 
Newton a definite property of a ray of light, immu- 
tably associated with the amount of refraction that it 
undergoes in passing from medium to medium. He 
attributed the colour of a body to the light by which 
the body is seen and not to the body itself, and was 


thus the first man to give a reasonably accurate 
account of this important matter. 

We have already seen that new ideas are not easily 
assimilated at any time, and this was particularly the 
case in the seventeenth century. Even men of science 
who were themselves original workers of great merit, 
failed to recognize in Newton's paper one of the 
finest contributions ever made to the theory of optics. 
Men of insignificant scientific stature raised objections 
to Newton's experimental results, and he answered 
carefully and with a good humour. This became 
irksome, and Newton began to lose patience. But 
Oldenburg induced him to go on, and to spend much 
time and energy in correcting his adversaries, and 
detecting their errors. Considerable discussion arose 
over the question of the five-time extension of the 
section of the beam. It was claimed by Lucas of 
Liege that he had carried out the same experiment 
as Newton and had obtained an extension of only 
three and a half times. Both Newton and his adver- 
sary maintained the accuracy of their measurements. 
There can be little doubt that both were right. The 
amount of " dispersion " depends upon the nature of 
the prism the kind of glass used. Some glasses give 
a much larger dispersion than others, for the same 
amount of general bending of the beam. This was not 
suspected by Newton. Had Lucas been fortunate 
enough to induce Newton to go into the question of 
the kinds of glass used by the two experimenters then 
a discovery of capital importance would have resulted. 

Newton's conviction that dispersion is always pro- 
portional to general deviation led him to conclude 
that it was quite impossible to eliminate chromatic 
aberration in a refracting instrument. This is now 
known to be untrue. By combining a convex lens of 
crown glass with a concave lens of flint glass we can 
make an achromatic combination, i.e. a combined lens 

THE OPTICAL DECADE, 1668-1678 69 

which gives an image almost (but not quite) devoid of 
colour aberration. If the mighty reflectors of to-day 
are monuments of Newton's genius in optical discovery, 
the mighty refractors of to-day are equally imposing 
monuments of the imperfection of Newton's know- 
ledge and the harm that accrues to science when the 
authority of a fallible human being is allowed to silence 
criticism and to discourage further research. It was 
only several generations after Newton's insistence upon 
the amount of dispersion being so-and-so, without 
paying any attention to the material of the prism, 
that his mistake was discovered and rectified. Since 
then refracting telescopes have become the really 
accurate instruments of astronomy, the mainstay of 
astronomical observation. 

In his account of the spectrum and the nature of 
colour Newton did not make any assumption as to 
the nature of light itself. He was content to speak of 
it as " something or other propagated every way in 
straight lines from luminous bodies." The experi- 
mental facts that he had discovered seemed to him to 
transcend any theory that one might invent concern- 
ing the ultimate nature of light propagation. When 
Robert Hooke, an Englishman of great ability whom 
we have already mentioned, and Christian Huygens in 
Holland, one of the most famous scientists of that 
century, raised objections to the spectrum on the 
ground of the wave-theory of light which they believed 
in, Newton felt that they were introducing irrelevances, 
and from men of their scientific power this was annoy- 
ing. He was always somewhat unwilling to face 
publicity and criticism, and had on more than one 
occasion declined to have his name associated with 
published accounts of some of his work. He did not 
value public esteem as desirable in itself, and feared that 
publicity would lead to his being harassed by personal 
relationships whereas he wished to be free of such 


entanglements. The effects of his publishing his 
optical results therefore decided Newton to desist from 
such publication in the future. " I see I have made 
myself a slave to philosophy. ... I will resolutely 
bid adieu to it eternally, excepting what I do for my 
private satisfaction, or leave to come out after me ; 
for I see a man must either resolve to put out nothing 
new, or to become a slave to defend it." Fortunately, 
Newton did not persist in this determination except 
for the fluxionary method and other pure mathematical 
work, which seem to have been doomed to remain the 
private possession of Newton and a few of his friends 
for a long time to come. 

We know very little of Newton's personal life 
throughout this period. We have, however, informa- 
tion on the authority of a close friend who shared rooms 
with him at Trinity, that Newton developed very early 
in life that forgetfulness about food and a carelessness 
about his own health which became characteristic of 
him in later life. He would often work till very late 
and miss restful sleep because of his work. At the 
age of thirty he was already turning grey. He 
suspected himself to be inclined to consumption and 
made medicines for his own use. Newton was indeed 
fond of dosing and curing himself. " His breakfast 
was orange peel boiled in water, which he drank as tea, 
sweetened with sugar, and with bread and butter." 
When Newton caught a cold he took to his bed and 
cured it by perspiration. All this reads like the life 
of a bachelor, far from the help of mother or wife, 
doing things for himself in a clumsy way and living for 
the work on which he is engaged. 

Newton was a kind man, sincerely pious and an 
influence for good in many ways. As regards his 
financial position, though he obtained various sums 
of money from his mother before being elected to 
the Lucasian chair, we may surmise that the scanty 

THE OPTICAL DECADE, 1668-1678 71 

yield of the farms at Woolsthorpe and Sewstern was 
not overmuch for the needs of Mrs. Smith and the 
three children by her second marriage. Newton was 
thus left to his own resources, which were not very 
great as his chair was only moderately endowed. 
He was also very free with his money, bestowing 
loans and gifts upon relations and friends with con- 
siderable liberality, and spending freely upon his 
scientific apparatus. 

It therefore became a matter of considerable concern 
to Newton that his College Fellowship was soon to 
expire, so that he would have to live upon the stipend 
of the Lucasian chair alone. In order to continue to 
hold his fellowship Newton would have had to go into 
holy orders. He declined to do this, and instead made 
an application to the King for a dispensation allowing 
him to retain the fellowship as a layman and as Lucasian 
professor. The petition was granted in April, 1675, an 
act of royal grace which does much to whiten the 
character of the merry monarch. 

Why did Newton refuse to go into orders ? He was 
a man of excellent character, sincerely and profoundly 
moral in his opinions and in his practices. He believed 
in the fundamentals of religion and even, as we shall 
see, wrote much on theological matters. It is clear that 
Newton desired as complete freedom in theological 
thought as in scientific belief, and refused to be bound 
in any manner. He did not accept without questioning 
all that was taught by the prevalent churches. His 
faith was that of a profound and independent thinker 
and investigator, seeking for the causes of all effects 
and for the unifying cause underlying all things, rather 
than that of an implicit believer in doctrines laid down 
by ecclesiastical authority. 

These economic disturbances of Newton's equanimity 
are mirrored in a remarkable manner by his relation- 
ship to the Royal Society. A fellow of this body had 


to pay an entrance fee of two pounds, and a continuous 
subscription of one shilling per week. In March, 1673, 
Newton wrote to the secretary Oldenburg resigning 
his membership. He gave as his motive the fact that 
he lived too far from London to be able to take full 
advantage of the meetings of the society. Oldenburg 
must have known better, for he offered to get Newton 
excused the shilling per week payment, and Newton 
himself raised no objection to an application to this 
effect being made to the Council of the Royal Society. 
Oldenburg did not present the application at once; 
possibly he waited to get a few more such applications 
to be dealt with at the same time. In January, 1765, 
he mentioned " that Mr. Newton was now in such 
circumstances that he desired to be excused from the 
weekly payments," and Newton and others including 
Robert Hooke were granted this relief. It is a 
pleasing thought that the greatest minds of the day 
had to submit themselves to what must have been 
felt as a humiliation in order to be relieved of the 
payment of one shilling per week I 

The scientist does not work for reward. The 
impelling motive is not personal gain or even personal 
fame : it is the insistent desire of the healthy human 
mind to know how Nature manifests herself around us, 
and the causes of these manifestations. Scientific men 
and women are continually giving of their best in the 
onward march of knowledge ; they place at the service 
of the community their powers and their energies. 
By membership of learned societies they even pay for 
the publication of the results which they deduce, often 
at their own expense and without interest or encourage- 
ment from anybody. Surely a community that has 
so much to spend on personal luxuries, and on fashion- 
able stars in the theatre and on the screen, could devote 
a little more on the fostering of scientific research and 
on making the task of the worker easier by removing 

THE OPTICAL DECADE, 1668-1678 78 

all anxiety of economic embarrassment ? Two and a 
half centuries have passed since then and some improve- 
ment has taken place in this respect, but Great Britain 
has much leeway to make up even now. 
[_The discovery of the spectrum was one of the most 
important events in the history of optics, and indeed, 
in the history of science. It has led to developments 
in all branches of natural knowledge) The discovery 
of the black lines in the solar spectrum early in the 
nineteenth century gave us spectrum analysis, which 
has revolutionized physics, chemistry and astronomy. 
Modern astronomy, rightly called ^Astrophysics, con- 
sists essentially of the application ofThe spectrum to 
heavenly phenomena. By its means we discover the 
constitution of the stars, their motions towards us 
and away from us, their distances when too remote to 
be measured directly, the events on the sun's surface 
which reveal electro-magnetic fields and disturbances 
of tremendous significance. The spectrum has by the 
work of Bohr and others given us an insight into the 
ultimate constitution of matter, and led to the initiation 
of the quantum theory, the implications of which we 
can as yet hardly guess. The spectrum has helped 
to establish Einstein's gravitational theory, and led to 
the discovery in the heavens of matter as immensely 
denser than the matter on our earth as the giant stars 
are lighter than our earthly matter. 

It is not possible in this book to give a detailed 
account of all Newton's optical work, and a mere 
catalogue of discoveries will convey little to the general 
reader. Yet a few words on some of Newton's 
work will illustrate the magnitude of his powers 
and the influence he exerted on subsequent develop- 

Newton not only applied the reflecting principle to 
the microscope, a suggestion that has not been very 
fruitful, but he also made the capital proposal that it 


would be an advantage when using ordinary refracting 
microscopes to employ light of one colour, or mono- 
chromatic light. While working with the plane mirror 
in his reflecting telescope Newton saw how imperfect 
reflection from a metallic surface is bound to be, and 
he hit upon an idea without which the powerful modern 
binoculars would be impossible. This was that in 
view of the high refractive index of glass, an isosceles 
right-angled prism of glass could be used as a reflector, 
giving much better results than metals. 

Discoveries of great theoretical importance were 
communicated to the Royal Society at the end of 
1675 in connexion with the colours of thin films of 
transparent matter. It is of course well known that 
very thin plates of transparent matter give different 
colours. The beauty of the soap-bubble has been 
immortalized in a famous picture. What are these 
colours due to ? Robert Boyle, famous for his law 
connecting the volume and pressure of a gas, and 
Robert Hooke, observed the phenomena in mica 
plates, but could not discover the relation between 
the colour produced and the thickness of the plate 
because of the extreme minuteness of the latter. 
Newton hit upon a beautiful and ingenious idea which 
we still use in our physical laboratories in Newton's 
rings and in other applications. 

The tangent to a circle at any point hugs the circle, 
and the deviation of the circle from it is very small 
even for considerable distances along the tangent, if 
the radius of the circle is large enough. If A is the 
point of contact of the tangent and P is a point not 
too far away on the circle, while PT is perpendicular 
to the tangent AT at A, then TP = TA 2 /2a where a 
is the radius, supposed large. Thus, if the radius is 
50 feet and TA is one-twentieth of an inch, we get for 
TP 1/480,000 of an inch. If TA is one-tenth of an 
inch, TP is 1/120,000 of an inch. If TA is an inch, 

THE OPTICAL DECADE, 1668-1678 75 

TP is 1/1200 of an inch. If then we take a flat glass 
plate and put into contact with it the spherical surface 
of a lens, with radius 50 feet, we have within a distance 
of one inch from the point of contact a film of air which 
varies from zero at the cenree to 1/1200 of an inch at 
the edge. Not only is the film thin enough to produce 


V2 Vl 


o: i 
< o 


Vi TV2 



* 5 * 

s I s 

o o 



FIG. 6 

Alternate bright and dark rings by transmitted light ; alternate dark and bright 
ngs by reflected light ; produced by thin air layer between a flat and a curved 


colours like those of the soap-bubble, but we can also 
calculate the thickness of the film at any measured 
distance from the point of contact. 

When Newton observed white light transmitted 
through the film or reflected from the film he saw 
coloured concentric rings, in which the colours were 
by no means so simply arranged as in the spectrum. 


On using light of one colour, however, the appearance 
became very much simplified, less beautiful of course, 
yet easier to understand. Newton found that by 
reflected light of any particular colour he got a circular 
dark patch in the centre, then a ring of that colour, 
then a dark ring, then another ring of that colour, 
then a dark ring again, and so on up to about twenty 
rings. With red light the successive radii were larger, 
with violet light they were smaller. Newton also 
found that the transmitted light gave a circular light 
patch in the middle, then a dark ring, then a light ring, 
then a dark ring, and so on, the radii being exactly 
the same for transmission and reflection in the case of 
any given coloured light, but lightness and darkness 
interchanging from one to the other. The radii were 
found to be proportional to the square roots of the 
successive numbers i, 2, 3, 4, etc., so that the air 
thicknesses at the successive circumferences were 
proportional to the numbers i, 2, 3, 4, etc. them- 

Newton at once concluded that a ray of light cannot 
have exactly the same properties at all points along 
its length. There must be variations in these proper- 
ties, " fits " as Newton called them. It is clear that 
a ray of light of any given colour prefers to be trans- 
mitted for a certain very short distance depending 
on the colour itself, then prefers to be reflected for an 
equal distance, then prefers to be transmitted for such 
a distance, and so on indefinitely. A ray of light thus 
has a space-period depending upon its colour, shortest 
for violet, getting longer for indigo, blue, green, yellow, 
orange, and being longest for red. 

One can think of many objections to this theory of 
fits ; but the most disconcerting feature about this 
matter is the way in which this experimenter of genius 
failed to grasp the (now) obvious implication of his 
beautiful experiment. Surely there must be a periodi- 

THE OPTICAL DECADE, 1668-1678 77 

city along a ray of light propagation, and this must 
be in the form of a wave, colour being in fact a property 
associated with the space-period or wave length ? 
Why did not Newton postulate a wave-theory and use 
the great principle of interference ? No great origin- 
ality was required, since both Hooke and Huygens 
had used the wave-theory in their controversies with 
Newton, and Hooke had even announced the principle 
of interference. 

Strange as it may appear to us now, Newton refused 
to accept a wave-theory of light. Did the opposition 
of Hooke and Huygens to Newton's discovery of the 
spectrum, based upon their wave-theory, prejudice 
Newton against such a view ? It is hardly credible, 
for Newton was too honest a thinker to be affected in 
this way. The fact is that Newton was severely 
practical in his conceptions. He always desired to see 
or feel, so to say, any natural force or other agency 
before he would accept it as an explanation of observed 
phenomena. His was the kind of mind that would 
interest itself in proving by direct observation the 
daily rotation of the earth and its annual revolution, 
that would have welcomed with tremendous joy 
Bradley's discovery of aberration as proving the latter 
and Foucault's pendulum as proving the former. 

Of course Newton was curious to explain why these 
fits existed and he did in fact invoke an " ether " to 
explain this and other phenomena. He supposed 
that a fluid ether permeates all space, whether occupied 
by matter or not, but that the density of the fluid 
varies from point to point. In this way Newton 
explained many properties of matter. As regards 
light he took it to be due to the very fast propagation 
of very tiny corpuscles, which are acted upon by the 
particles of the ether and so receive this property of 
alternate fits of preference for transmission and for 
reflection. This view he expressed in 1675 and he 


developed it a few years later in a letter to Robert 
Boyle. Apparently, however, an ether the existence 
of which he could not prove directly, was not 
palatable to Newton, and he rejected the ether 
to be revived later in query form when universal 
gravitation was added to the things requiring ex- 

By means of his theory of fits Newton was able to 
make considerable advance in the explaining of trans- 
parency and opacity, and of the colours of different 
bodies. Transparency and opacity depended, accord- 
ing to Newton, upon the sizes of the spaces between 
the ultimate particles of a body, while the colour of 
the body depended upon the sizes of the ultimate 
particles themselves. It would take us too far to 
discuss these views in detail. One thing we can say, 
however : they represented the first rational set of 
opinions ever put forward on the subject, and 
were a tremendous advance on the views held 
at that time by the greatest of physicists and mathe- 

Another important optical experiment carried out 
by Newton referred to what we" nowadays call diffrac- 
tion. Light is supposed to travel in straight lines so 
long as no refraction takes place. Hence, in uniform 
and still air no deviation from rectilinear propagation 
should occur. This is not the case. Light rays do 
bend round a corner just as sound bends round a 
corner. In the case of light, however, the bending 
can be detected only by means of very careful observa- 
tion. An Italian, Grimaldi, first obtained the bending 
and the result was published in 1665. In 1674 Hooke 
carried out further experiments and betrayed his genius 
by suggesting the principle of interference in order to 
explain the phenomenon. Newton carried out diffrac- 
tion experiments at about the same time. He cast 
the shadow of a human hair upon a screen and found 

THE OPTICAL DECADE, 1668-1678 79 

the shadow to be much wider than the thickness of 
the hair, and to exhibit coloured fringes. He did not 
accept Hooke's explanation which is the right one 
and attributed the phenomenon to the possibility of 
flexibility in a ray of light. Rays of different colours 
have different flexibilities. As a ray passes the edge 
of a body a wave-like effect is produced on the ray, 
giving it a shape like that of an eel ! Rectilinear 
propagation is upset, and colours are introduced. This 
queer explanation was published nearly thirty years 
later in Newton's " Optics." 

Why Newton should have been reluctant to accept 
the wave-theory of light, while prepared to postulate 
these eel-like motions, it is difficult to explain. Personal 
idiosyncrasy is as much the prerogative of genius as 
of lesser minds. Newton filled the universe with an 
ether in order to account for the fits in a remote and 
indirect manner. Yet he declined to follow Huygens 
and Hooke in the wave-theory and in interference. 

The consequences to science were very unfortunate. 
When Newton had become famous as the discoverer 
of the law of universal gravitation and had explained 
the motions of the planets in a manner unique in 
scientific history, the prestige of Hooke and of the 
great Huygens could not prevail against his renown. 
The wave-theory of light fell into disrepute. It was 
not till more than a century later that the theory was 
rehabilitated by the work of the Englishman Young 
and the Frenchman Fresnel. The hero-worship 
accorded to genius has its vicious as well as its virtuous 
side. For genius is but human after all : it is liable 
to honest mistake and even to prejudice and to passion. 
Science should stand above all human considerations. 
It must not bend the knee to any human authority. 
It must rest on honest research, based upon complete 
intellectual independence. The raw schoolboy may be 
right where the sage of mighty repute is mistaken. 


The weight of Newton's authority delayed optical 
progress for many generations. It was not Newton's 
fault, of course ; it was the fault of the lesser men 
who followed him and mistook idolatry for sincere 


If with giddier girls I play 
Croquet through the summer day 

On the turf, 

Then at night ('tis no great boon) 
Let me study how the moon 

Sways the surf. 

MoRriMER COLLINS : ' Chloe, M.A.." 

WE now enter upon the second or gravitational 
decade of Newton's scientific career. The 
period between 1668 and 1678 was not exclus- 
ively devoted to optics. His famous paper on the 
method of infinite series and fluxions was written in 
1669. He wrote a second treatise on fluxions in 1672, 
but this also remained unpublished. He communi- 
cated with Huygens concerning gravitation in January, 
1673, and he wrote a paper for the Royal Society on 
the excitation of electricity in glass in 1675. In the 
same year Newton wrote to Nicolas Mercator, immor- 
talized in the map projection called after his name, 
concerning the librations of the moon, the fact, namely, 
that although on the whole the moon always turns the 
same half of its surface to the earth, we do notice 
slight changes in this respect, as if the moon were 
oscillating from one side to the other. Newton 
explained this satisfactorily as being due to the uniform 
rotation of the moon about its axis in exactly the time 
it takes to complete a revolution round the earth 
this motion of revolution is not uniform, so that some- 
times the moon has apparently rotated too much, at 
6 8z 


other times too little, in relation to the angle through 
which it has revolved round the earth. 

In the midst of his scientific preoccupations Newton 
even found time to discuss agricultural matters. He 
was perhaps making inquiries on behalf of his college, 
but in September, 1676, he wrote to Oldenburg on the 
question of planting apple trees for the manufacture 
of cider 1 He wished to know : " What sort of fruit 
are best to be used, and in what proportion they are 
to be mixed, and what degree of ripeness they ought 
to have ? Whether it be material to press them as 
soon as gathered, or to pare them ? Whether there 
be any circumstances to be observed in pressing them ? 
or what is the best way to do it ? " 

In the same year Newton wrote to the great German 
philosopher and mathematician, Leibnitz, concerning 
his method of fluxions. Leibnitz sent a reply in which 
he gave an account of the differential calculus with the 
notation in vogue to-day, and which Newton must at 
once have seen to be the same thing as his own fluxions, 
differing from his invention only in the notation. 

But Newton's attention was soon directed to astro- 
nomy and gravitation. We may assume that the 
abortive calculations made at Woolsthorpe in 1666 
never quite dropped out of his memory. The problem 
of planetary motions was too insistent and the failure 
too tantalizing to leave a man like Newton quite 
unaffected. Meanwhile another man had been writing 
on the subject, Robert Hooke. 

Hooke was a man of great genius, but owing to his 
preoccupation with all sorts of matters he never quite 
finished off any great line of research, and consequently 
never reaped the full fruits of the seeds that he sowed. 
Newton was on the other hand a remarkably successful 
investigator of singular stability of character and 
steadiness of application. We have already seen that 
Hooke and Newton had had occasion to dispute over 


optical matters. Hooke had also treated the younger 
Newton somewhat unkindly on the occasion of his 
first communication to the Royal Society, when 
Newton's reflecting telescope was under inspection. 
Hooke may have seen in Newton the younger and 
greater rival who did the things that Hooke might 
have done if not anticipated by Newton. A mild 
jealousy of Newton grew up in Hooke's mind, and 
perhaps a slight suspicion of Hooke entered Newton's 

Similar unfortunate circumstances arose soon in 
connexion with gravitation. While Newton was specu- 
lating on his failure at Woolsthorpe, Hooke sent to the 
Royal Society, in 1666, a paper on the question of 
how the earth's gravity varies with height above the 
earth, making the important suggestion that the force 
of gravity could be measured by means of a " swing 
clock ' ' or pendulum. He followed this up with another 
paper in the same year, suggesting that the planetary 
motions could be explained by means of an attraction 
towards the central body. This vague idea, which 
had occurred to several others before then, took more 
definite shape in a third publication which appeared 
in 1674. In this work Hooke quite definitely postu- 
lated universal gravitation, stating that each heavenly 
body not only keeps itself together by its own attrac- 
tion, but also exerts a force upon every other heavenly 
body. He did not yet know what law to use, how the 
gravitational force exerted by a body depended upon 
the distance from this body ; but in 1679 Hooke wrote 
to Newton and made the assertion that if the earth's 
gravitation varied inversely as the square of the 
distance the curve described by a projectile would be 
an ellipse, with a focus at the centre of the earth. 

In spite of all this, however, Hooke's claim to 
consideration in the question of priority in this 
matter could have been of little weight. Newton had 


discovered the inverse square law thirteen years before 
by direct deduction from Kepler's third law of planetary 
motions. He had been held up by a quantitative 
discrepancy which turned out to be due to a quite 
irrelevant circumstance, namely, his ignorance of the 
correct size of the earth. Hooke's suggestion that the 
inverse square law would yield elliptic motion round 
a focus was not accompanied by a proof. It was 
Newton who established independently, and by 
brilliant mathematical reasoning, that all the facts of 
planetary motion then known could be accounted for 
by universal gravitation according to the inverse square 
law. By universal consent Newton was acclaimed as 
the discoverer of the secret of heavenly mechanics. 
This reacted upon Hooke's mind with some unpleasant 

If Newton had been acquainted with correct values 
of the earth's radius published thirty years before 
his Woolsthorpe calculations, would he have made 
his great gravitational achievements much earlier ? 
Possibly in his Lincolnshire exile Newton had no means 
of referring to books on the subject, but when he did 
get back to Cambridge he should have become 
acquainted with the correct radius of the earth. 
Accurate measurements by the Frenchman Picard 
were communicated to the Royal Society on January 
n, 1672, the very meeting at which Newton was 
elected a fellow and at which his reflecting telescope 
was exhibited, and published in the Transactions in 
1675 : Newton cannot have missed seeing these results. 
It is a remarkable fact nevertheless that he did not 
take up the matter again until his attention was 
directed to it by Hooke himself. 

Robert Hooke became Secretary of the Royal Society 
in 1678, after Oldenburg's death. He wrote to Newton 
asking him if he had something new to communicate 
to the society. Newton replied with a dissertation on 


the diurnal rotation of the earth. The reason why the 
earth's rotation remained undiscovered till so recently, 
and why some cranks still doubt it to-day, is simply 


/ / ^ 



FIG. 7 


Path of stone dropped from A lies in that plane through the centre of the earth 
which touches B's circle of latitude at the point B. The stone falls east of B' (the 
new position of B when the stone reaches the ground) and south of it. 

that this rotation takes place in a perfectly smooth 
manner, with all the things on the earth accompanying 
it in its rotation. No differential motions are visible 


to us : the solid earth rotates, the waters of the ocean, 
the air, houses, trees, we ourselves all goes with the 
earth. How can the supposed rotation be distinguished 
from a state of rest of the earth ? 

It was Newton who saw that this very fact that all 
things on and near the earth accompany it in the 
diurnal rotation could be used to demonstrate the 
rotation ocularly. For consider a point A vertically 
above any point B of the earth's surface, so that AB 
is along the extension of a radius from the earth's 
centre. In the diurnal rotation the line AB is carried 
with it bodily ; hence the point A has a velocity, due to 
this rotation, greater than that of B, since it is further 
than B from the common axis of rotation. Now let 
a body be dropped at A. During the fall it receives 
downward acceleration taking it to B. But it also 
had initially a horizontal velocity west to east greater 
than that of B. Hence the falling body will not reach 
the earth exactly on B, but slightly to the east of B. 
The deviation would be very small indeed : for AB = 
100 feet, the deviation in London would be T V inch. 
Newton suggested this as a possible experiment a 
straightforward test of the earth's rotation. 

The suggestion was adopted and Hooke was 
appointed to carry it out. Before doing so, however, 
he examined the matter more carefully and came to 
the conclusion that Newton was not quite right. If 
B is on the Equator, then Newton's argument is 
faultless. But if B is not on the Equator, then the 
deviation will not be exactly to the east : it will be 
also a little to the south in the northern hemisphere, 
to the north in the southern hemisphere. It is not 
difficult to understand why this should be the case. 
The body during its fall is pulled along AB. Relative 
to B the initial motion of A is to the east. Hence the 
body's fall takes place in the plane containing the line 
AB and touching the cone described by AB, along the 


line AB. This tangential plane lies outside the cone 
and so cuts the earth in a circle which lies outside the 
parallel of latitude at B : in other words, the body 
must come a little south as well as east, since it is the 
parallel of latitude that defines east and west. 

Newton had missed this point, and at once admitted 
it when his attention was drawn to it. Hooke carried 
out the experiment and verified the deviation in 
December, 1679, the first ocular proof in history of 
the rotation of the earth ! It was the year of the 
Habeas Corpus Act. 

In connexion with this investigation the question 
arose between Newton and Hooke as to what the path 
of a body actually is under the earth's attraction, 
taking this attraction to vary inversely as the square 
of the distance. Newton conjectured that the path 
would be a spiral curve. Hooke dissented from this 
and asserted that the path would be an ellipse with a 
focus at the centre of the earth. Newton himself said 
about this : " And tho' his (Hooke's) correcting my 
spiral occasioned my finding the theorem, by which 
I afterwards examined the ellipsis : yet am I not 
beholden to him for any light into the business, but 
only for the diversion he gave me from my other 
studies to think on these things, and for his dogmatical- 
ness in writing, as if he had found the motion in the 
ellipsis, which inclined me to try it, after I saw by 
what method it was to be done." 

It is clear that Hooke could not prove his assertion : 
it was a guess, based upon his extending the idea of 
Kepler's laws of planetary motion to the motion of a 
projectile under the earth's gravitation. For this 
Hooke deserves great credit, yet the real discoverer 
was Newton, for it was Newton who turned Hooke's 
useless guess into a certainty, being impelled thereto 
by Hooke's " dogmaticalness in writing." Newton 
was able to construct a proof of the proposition that a 


body moving under an attraction towards a fixed point 
varying as the inverse square of the distance from this 
point, describes an ellipse with a focus at the centre of 

This was a result the importance of which could 
hardly be exaggerated, and Newton should have 
proceeded now to complete a theory of the solar 
system. But, having proved the elliptic motion, 
Newton " threw the calculations by, being upon other 
studies ; and so it rested for about five years." He 
was making alloys for metallic mirrors one can only 
wonder whether they were important enough to make 
Newton " throw by " the calculations upon which his 
greatest fame in human history was destined to rest. 
He corresponded with the Astronomer Royal, Flam- 
steed, about the great comet of 1680, and the views 
Newton then expressed make it clear that he had not 
yet reached a correct understanding of cometary 
motions. If he had paid more attention to the train 
of thought roused by Hooke, he would not have held 
these erroneous views. 

No apology need be offered for Newton's apparent 
indifference to the matter. Evidently he was still 
under the influence of his Woolsthorpe failure to 
explain the moon's motion by the earth's gravity. 
He could not deal with the motions of the planets 
under an attraction towards the sun, without dealing 
at the same time and on the same principle with the 
moon's motion round the earth. To Newton's practical 
mind the latter was even the more important aspect, 
for only in the case of the earth's gravity could he 
examine a really obvious and measurable force a force 
that enters into all the phenomena of daily life. So 
long as the moon did not respond to his calculations 
he had no right to postulate universal gravitation as 
the cause of the planetary and lunar motions. 

For some reason or another Newton's attention had 


not been drawn to the more correct value of the earth's 
radius. He had taken it to be given by sixty English 
miles for a degree of latitude. The correct value is 
much more. Picard's value was 69-1 miles, a difference 
of over fifteen per cent. It would not have escaped 
the notice of a mind like Newton's that this was just 
the quantity required to correct his calculations of 
1666. Yet it was not till June, 1682, that Newton 
became fully aware of Picard's measurements or was 
it that only then did it strike him how these measure- 
ments would affect his calculations ? We are told 
that at a meeting of the Royal Society in June, 1682. 
conversation turned upon Picard's work. Newton 
noted the result and on his return to Cambridge took 
up the Woolsthorpe calculations once again. Becoming 
conscious of the approaching almost perfect agreement 
between his theory and fact, Newton, the story relates, 
became so agitated that he was forced to entrust the 
arithmetic to a friend. Eventually the truth emerged. 
The force which drags the apple to the earth is the 
force that directs the moon round the earth. The 
daring suggestion that the heavenly bodies move under 
the same kind of forces and obey the same laws of 
motion as the earthy matter around us was vindicated. 
The road became quite clear for what may be described 
as the grandest generalization ever made in human 

Apparently Newton hardly ever published a dis- 
covery without being urged to do so by others. Even 
when he had arrived at the solution of the greatest 
problem that astronomy has ever had to face he said 
nothing about it to anybody. Fortunately other men 
were interested in the same problem. These were the 
three Englishmen, Robert Hooke, Sir Christopher 
Wren, excellent mathematician and brilliant architect, 
and Edmund Halley. Edmund Halley was twelve 
years younger than Newton, and a man of great 


ability, who, in 1684, had already done a number of 
important pieces of scientific and astronomical work, 
especially on comets. He became interested in the 
problem of gravitation and in January, 1684, he 
deduced from Kepler's third law that the sun's gravi- 
tation must vary inversely as the square of the distance 
in other words, he did in 1684 what Newton had 
done in 1666. He tried to deal with the much more 
difficult problem of finding the path of a body moving 
under such an attraction, but he failed. He therefore 
sought out Wren and Hooke and asked them if they 
could supply what he could not achieve. Apparently 
both of them had deduced the inverse square law from 
Kepler's third law. But as regards the question of 
finding the path under such an attraction, Wren 
admitted he could do nothing with this bigger problem, 
while Hooke made the statement that upon the inverse 
square law " all the laws of the celestial motions were 
to be demonstrated, and that he himself had done it." 
Wren thereupon made a sporting offer that if Hooke 
or Halley could produce the mathematical proof, 
instead of the mere assertion, within two months, he 
would present the discoverer with a book of forty 
shillings. Hooke again said " he had it, but that he 
would conceal it for some time, that others trying and 
failing might know how to value it when he should 
make it public." But he never produced any such 
proof, and Halley, tired of waiting for it, decided to 
apply to Newton. 

The momentous interview took place in August, 
1684, about half a year before the death of King 
Charles II. Halley visited Newton at Cambridge, and 
came straight to the object of his visit. " What would 
be the path of a planet under a gravitational attraction 
varying inversely as the square of the distance ? " he 
asked. " An ellipse," came Newton's reply without 
hesitation. " How do you know ? " asked Halley. 


" I have calculated it," answered Newton. Halley 
naturally wanted to see the proof, but Newton had 
apparently not paid much attention to the matter for 
some time and so could not immediately find his notes 
on the subject. He promised to let Halley have the 
proof soon. 

Was Halley confident that Newton's proof would 
really be forthcoming ? After all, his success with 
Newton was not very dissimilar from his success with 
Hooke, who had also claimed to have a proof and had 
not yet produced it. The fact that Halley took the 
trouble to go to Cambridge to see Newton shows, 
however, that already he had learned to admire 
Newton's genius and that he had complete confidence 
in Newton's ability to establish any claim he might 
make. In this he was not disappointed. Newton could 
not find his original notes, but he constructed the proof 
again after a little trouble and sent it to Halley 
within three months of the latter's visit to him. 

Halley 's joy was unaffected. He was a man who 
could see gladly the success of another greater than 
himself. He decided that such a discovery could not 
remain unpublished. He visited Newton again and 
found that the latter had meanwhile prepared a brief 
account of the motion of a body under a force directed 
to a fixed centre, particularly when the force varies 
inversely as the square of the distance, in which case 
the path is a conic with a focus at the centre of force. 
Newton had already lectured on the subject as Lucasian 
professor. Halley made Newton promise to send this 
short treatise " De Motu " to the Royal Society, a 
promise that was communicated to and welcomed by 
the society on December 10, 1684. 

Great events were taking place in England then. 
Surrounded by intriguing parties who demanded 
opposite kings, the King was in perplexity both as to 
his foreign relationships and as to the question of 


summoning Parliament to learn the will of his people. 
In the midst of it all, on February 6, 1685, the King 
died of apoplexy. He was buried in Westminster 
Abbey eight days later, and a perplexed people saw 
with mixed feelings the accession of Charles' brother, 
King James II. It has been said that the reign thus 
ended was the worst reign in English history : yet let 
us remember that Charles had founded both the Royal 
Society and the Royal Observatory, Greenwich, and 
that he had had the grace to do an act of decency to 
Newton in allowing him to retain his Trinity fellowship 
without going into orders. 

It was in the midst of this national commotion that 
Newton wrote out his paper on planetary motions, and 
it was received by the Royal Society while the dead 
King was awaiting burial. Newton himself indicated 
that he was preparing a larger treatise on the subject, 
and in April, 1685, he began the preparation of his 
great work. 

Newton was forty-two years of age and at the very 
height of his mental powers. If he showed greatness 
as a physical experimenter in his optical work, he was 
soon to prove himself even greater as a physical and 
mathematical thinker. Let us state clearly what was 
involved in the task he had undertaken. In the first 
place, the principles of dynamics had to be thoroughly 
grasped and clearly formulated, namely, that the 
absence of force or the balancing of the forces acting 
on a body means uniform speed in constant direction, 
without any acceleration, while any change in speed 
or in direction of motion of a body must be accounted 
for by a force or resultant of forces, proportional to 
the acceleration and acting in the same direction. 
Secondly, the type of force appropriate to the problem 
of planetary motion had to be considered and the 
inverse square law deduced. Thirdly, the physical 
reality of this attraction had to be proved, as presented 


by the motion of the moon round the earth, the 
gravitational effects of which we experience daily and 
can measure accurately. Fourthly, the law of gravi- 
tation had to be applied in its general form to the 
planets and the motions as given by Kepler's laws 
accounted for accurately. For this purpose new and 
more powerful mathematical methods were required, 
and Newton had to invent them. Finally, the whole 
solar system had to be considered under the aspect of 
universal gravitation, and motions of satellites and 
comets explained, precession and tides brought within 
the ambit of scientific research. 

A mighty task this was which could be accomplished 
only by a man specially favoured by the gods. Popular 
imagination has been captured by the third point, the 
association of the moon's motion with the fall of the 
apple and rightly so, for this physical extension from 
the earthly to the celestial is one of the most significant 
steps in the revolution of ideas that Newton's work 
has brought about. But what exhibited Newton's 
powers to the full were the fourth and fifth points on 
which he laboured during the next two years. 

Newton was not content with the astronomical 
observations of the older astronomers, and fortunately 
he found at hand a man prepared to give him the 
latest and best results. This was John Flamsteed, 
whom we have already mentioned as having corre- 
sponded with Newton a few years before about comets. 
He was a remarkable observer of the heavens and was 
appointed Astronomer to King Charles II at the early 
age of twenty-nine, in 1675. The Greenwich Observa- 
tory was buijt and Flamsteed headed the line of 
eminent astronomers that have adorned the post of 
Astronomer Royal. It was Flamsteed who gave 
Newton the best information possible about the orbit 
of Saturn, about the motions of the satellites of 
Jupiter and Saturn the only satellites then known 


besides the moon about the tides, about the flattened 
appearance of Jupiter's disc. For many years New- 
ton depended upon Flamsteed for the facts upon 
which he built up the law of universal gravitation, and 
verified the consequences that flowed from the law. 

The first part of the work was soon ready ; it was 
the treatise " De Motu " more fully developed, forming 
Book I of the complete work. The second part or 
Book II was ready by the middle of the year 1685. 
Both books dealt with the theoretical aspects of 
dynamics, especially as required for application to 
astronomy. The third part, or Book III, was a much 
more difficult task, as in it Newton had to give detailed 
applications of his theory to the observed planetary 
motions and other phenomena in the heavens. Finally, 
on (April 21, 1686, Halley announced to the Royal 
Society that " Mr. Isaac Newton has an incompar- 
able Treatise of Motion almost ready for the press." 
On April 28th a manuscript entitled " Philosophise 
Naturalis Principia Mathematica " (The Mathematical 
Principles of Natural Philosophy) was presented to the 
society^JAs a matter of fact, this manuscript only 
contained Book I, but the importance of the whole 
work was speedily recognized and Halley was asked 
to report to the Council on the question of having the 
book printed. As the Council dallied in the question, 
the society resolved, at its meeting of May igth, 
" That Mr. Newton's work should be printed forthwith 
in quarto." Still nothing was done, and on June 2nd 
the society adopted a most remarkable resolution : 
" That Mr. Halley undertake the business of looking 
after it, and printing it at his own charge, which he 
engaged to do " ! 

This is an interesting sidelight on the way scien- 
tific men who are enthusiastic about their subjects 
are prepared to face personal inconvenience and 
loss in the furthering of their aims. Halley was not a 


particularly rich man and he had a wife and family. 
But when he realized the state of the Royal Society's 
finances he guessed that Newton's book would never 
be printed if it had to depend upon the society defraying 
the cost. Apparently the Royal Society had depleted 
its exchequer by printing a work on fishes, and in spite 
of the members' admiration for Newton's work they 
could not muster enough enthusiasm to give this 
admiration a practical form. Halley therefore decided 
that cost him what it may the book must be printed, 
and just as Halley had discovered Newton's genius in 
the matter of his gravitation theory, so it was Halley 
who took the risk of shouldering the financial burden 
involved in giving it to the world. 

Halley was a distinguished man of science in his 
own right, and was to occupy the highest astronomical 
post in England, that of Astronomer Royal, and to 
give to the world the first prediction of the return 
of a comet. Yet, if Halley had done nothing more 
than secure the publication of the " Principia " he 
would have been assured of the everlasting gratitude of 

If Halley in this way shielded Newton from financial 
worries, he could not shield him from other unpleasant- 
ness. Amidst the eulogies that greeted the presenta- 
tion of Newton's manuscript, a discordant note had 
been struck by Hooke. We can easily imagine the 
feelings of Hooke at seeing the prize for which he so 
ardently yearned snatched from his grasp. While he 
had been speculating, Newton had worked and reached 
a happy conclusion of his labours. Hooke could not 
deny the great value of Newton's mathematical proof 
that the inverse square law of universal gravitation 
explains all the planetary motions then known, but 
he claimed that the idea to use the inverse square law 
had been given to Newton by himself. 

This was really a foolish claim to make, since the 


fundamental idea had occurred to several people before 
Hooke, and even in Hooke's time there were Halley 
and Wren who had deduced the inverse square law 
from Kepler's third law independently of himself and 
of one another. It was therefore very likely that 
Newton, whose genius was known to excel that of any 
one of this trio, had discovered this for himself, before 
Hooke had suggested the inverse square law to Newton 
in 1679. As we know, Newton made this discovery as 
early as 1666, and when told of Hooke's claim, Newton 
lost his equanimity and usual sense of fairness to such 
an extent as to retort that, so far from Hooke having 
suggested the inverse square law to Newton, Hooke 
had got the first idea of this law from others, and even 
from a letter that Newton had written to Huygens on 
the subject in 1673, through the secretary of the 
Royal Society, Oldenburg, and a copy of which Hooke 
must have seen when he succeeded Oldenburg. But 
Halley did all he could to prevent a scandal, and 
finally Newton inserted into his book a statement that 
the inverse square law had been deduced from Kepler's 
third law of planetary motions by himself, and inde- 
pendently by Wren, Hooke and Halley. 

This further unpleasantness in respect to scientific 
work caused Newton much pain and he wanted to 
suppress Book III, "De Mundi Systemate," containing 
direct applications of the inverse square law to planet- 
ary theory, lunar theory, the theory of comets, tides, 
etc. Fortunately, Halley's good sense succeeded in 
preventing such a calamity, and Newton proceeded 
with the plans originally made. On July 6, 1686, the 
imprimatur, or license to print the book in the name 
of the Royal Society, was given by the then President, 
the famous diarist, Samuel Pepys, and within a couple 
of weeks the work of printing Book I began. Book II 
reached the Royal Society in March, 1687, and Book III 
in April of the same year. 


Newton's work at the " Principia " was interrupted 
by an event of political importance. The accession to 
the throne of King James II was soon followed by an 
attempt on the part of the King to favour his fellow 
Catholics in violation of the law of the land. If we 
can now look with more detached eyes at this exercise 
of the royal will, and admit that religious tests of any 
kind are to be condemned, and acts of exclusion against 
any church are equally undesirable, we cannot treat 
the King's attempt to force his will upon the univer- 
sities in the same way. A university is a living 
monument to knowledge and truth, the degrees and 
diplomas awarded by a university can be granted only 
on proof being supplied of learning or research on the 
part of the candidates for such honours. The only 
persons qualified to judge the fitness of candidates are 
the professors of the university : deprive them of this 
monopoly, infringe in any way upon their free and 
unfettered decision in academic matters, and the 
prestige of the honours awarded at their hands is 
lowered and the university loses in status and dignity 
as the repository of knowledge. 

James had already forced the University of Oxford 
to accept as a high academic official a man who had 
no qualification for occupying such a post, but who 
was a Roman Catholic and as such was a nominee of 
the King's. In February, 1687, the blow fell upon 
the University of Cambridge. The particular form 
that the King's attack took would leave us cold 
nowadays, since it really amounted to removing 
restrictions against Catholics as such. But the prin- 
ciple at stake was one that overshadowed the actual 
issue in the dispute. The Vice-Chancellor of the 
University declined to carry out the royal mandate 
to confer the degree of M. A, upon a certain Benedictine 
monk without his taking the oaths of allegiance 
and supremacy. Finally, the Vice-Chancellor was 



summoned to appear before the High Commission 
Court at Westminster, accompanied by representatives 
of the Senate of the University. Newton was one of 
the eight representatives chosen for the purpose, and 
he maintained a firm determination not to submit and 
not to accept any compromise. 

The infamous Judge Jeffreys presided over the court. 
The Vice-Chancellor was soon reduced to silence ; the 
other deputies were forbidden to say anything in defence 
of the attitude of the University, and ordered out of 
court. " As for you/' said Jeffreys to them, " most 
of you are divines. I will therefore send you home 
with a text of Scripture, ' Go your way and sin no 
more, lest a worse thing happen to you/ " The greatest 
man of the century, not a " divine/' was among the 
Cambridge representatives thus insulted, the man who 
was just then putting the finishing touches to the book 
that will outlive scores of royal bullies like James, and 
foul-mouthed brutes like Jeffreys. The Vice-Chancellor 
was not only deprived of his office, but also lost his 
post as Master of Magdalen College, although the 
University ultimately succeeded in its resistance. 

Newton went back to his rooms between the great 
gate and the chapel at Trinity and proceeded with the 
proof reading and other tasks in connexion with the 
publication of the " Principia." Within two months 
of Newton being ejected ignominiously from the court 
presided over by Jeffreys, the " Principia " was 
published, dedicated to the Royal Society " flourishing 
under his august Majesty James II " ! 

Newton was then forty-four years of age. He had 
spent over twenty years in the pursuit of truth, mainly 
in optics and in gravitation theory. He had remained 
a bachelor, possibly by inclination ; but certainly in 
accordance with the peculiar traditions that were in 
force till only half a century ago, and which prevented 
a college fellow leading the normal life of a human 


being. He had remained poor in accordance with the 
general practice of civilized humanity, that is content 
to let its men of genius give their all to humanity and 
receive nothing in return. Newton had reached middle 
age in a state of semi-obscurity, known to the few like 
Halley, Wren, Huygens, Leibnitz and Hooke, but un- 
recognized by the masses whose adulation is blindly 
bestowed and equally blindly withheld. 

On the evidence of his relation, assistant and 
amanuensis, Humphrey Newton of Grantham, who 
was with Isaac Newton from 1683 to 1689, we know 
that Newton was " very meek, sedate, and humble, 
never seemingly angry, of profound thought, his 
countenance mild, pleasant, and comely. f ' He delivered 
his lectures to the few who cared to hear them, dictating 
for half an hour as rapidly as his audience could write ; 
and if nobody came he went back to his work. He took 
no recreation or had any pastime, devoting all his time 
to his work. " He ate very sparingly, nay, ofttimes 
he has forgot to eat at all, so that, going into his 
chambers, I have found his mess untouched. ... He 
very rarely went to bed till two or three of the clock, 
sometimes not till five or six, lying about four or five 
hours, especially at spring and fall of the leaf, at which 
times he used to employ about six weeks in his elabora- 
tory, the fire scarce going out either night or day, he 
sitting up one night and I another, till he had finished 
his chemical experiments. 

" I cannot say I ever saw him drink either wine, ale, 
or beer, excepting at meals, and then but very spar- 
ingly. He very rarely went to dine in the hall, except 
on some public days, and then if he has not been 
minded, would go very carelessly, with shoes down of 
heels, and his head scarcely combed. ... He was 
very curious in his garden, which was never out at 
order, in which he would at some seldome time take a 
short walk or two, not enduring to see a weed in it." 


This garden was the space between the road and the 
college on the right-hand side on entering the great 
gate at Trinity College, and contained his chemical 
laboratory. " In his chamber he walked so very much 
that you might have thought him to be educated at 
Athens among the Aristotelean sect. ... He kept 
neither dog nor cat in his chamber." This disposes of 
the well-known story that Newton made a hole in the 
door for his cat to get in and out without disturbing 
him, and then when the cat had kittens, made another 
and smaller hole for the kittens to get through ! 

Newton's refusal to go into holy orders is illuminated 
by the following : "He very seldom went to Chapel, 
that being the time he chiefly took his repose ; and, 
as for the afternoon, his earnest and indefatigable 
studies retained him, so that he scarcely knew the 
house of prayer. Very frequently, on Sundays, he 
went to St. Mary's Church, especially in the fore- 
noon. ... As for his private prayers I can say 
nothing of them ; I am apt to believe his intense 
studies deprived him of the better part." But busy 
as Newton might be he had time for charitable deeds, 
and " few went empty handed from him." He helped 
poor relations and neighbours most generously, tipped 
the college porters frequently, although he never broke 
their rest by coming in late at night. He was patient 
and conscientious an eminent example of the great 
worker prosecuting his studies quietly, and little 
dreaming that his discoveries were to become the 
glory of mankind. 


Nec fas est propius mortal! attingere divos. 


THE "Principia" appeared in July, 1687, in 
one small quarto volume containing 500 pages. 
It was illustrated with a large number of 
diagrams in the form of woodcuts, was issued bound in 
calf, and was sold at nine shillings per copy. Halley's 
generosity to and admiration for Newton are both 
apparent from the following, taken from a letter 
written by the former on July 5, 1687 : " I have 
at length brought your book to an end, and hope it 
will please you. The last errata came just in time 
to be inserted. I will present from you the book 
you desire to the Royal Society, Mr. Boyle, Mr. 
Paget, Mr. Flamsteed, and if there be any else in 
town that you design to gratify that way ; and I have 
sent you to bestow on your friends in the University 
20 copies, which I entreat you to accept. ... I hope 
you will not repent you of the pains you have taken in 
so laudable a piece, so much to your own and the 
nation's credit, but rather, after you shall have a little 
diverted yourself with other studies, that you will 
resume those contemplations wherein you had so great 
success, and attempt the perfection of lunar theory, 
which will be of prodigious use in navigation, as well 
as of profound and public speculation." 

In view of King James II having been Lord High 



Admiral early in his brother's reign and the probable 
value of Newton's work in navigation, a copy of the 
" Principia " was presented to the King by Halley. 
Did James make much use of it in his many voyages 
across the sea after his indignant subjects had driven 
him out of the country sixteen months later ? 

The great classics of science are rarely read in sub- 
sequent generations. Whereas the young school boy 
or girl is introduced to Milton's work in the original, 
and learns, if judiciously taught, to admire and per- 
haps to emulate the great lines of our incomparable 
national poet, no boy or girl at school ever sees a copy 
of the book written by his junior contemporary, 
Newton. We do not blame modern educationists 
for preferring modern books on mathematics and 
science as text-books for modern pupils. The con- 
tinued progress of science forces us to modernize, to 
condense and to systematize the mathematical and 
scientific knowledge of the past in a manner suitable 
for the consumption of present-day learners. Yet one 
would wish that a little time could be found to introduce 
the pupils of our schools, and especially of our univer- 
sities, to the actual words of the great original thinkers 
in science. If scientific results are impersonal and 
objective, scientific research embodies the mind, the 
soul, of the worker, and the essence of education is 
surely the bringing to bear upon one mind the influence 
of another mind, a forerunner in the search for 

The " Principia " was written and issued in Latin, 
the international language of learning till a few genera- 
tions ago. Newton was not only a discoverer of 
unique power, but also an elegant exponent of his 
views. Said Laplace, the great scientific representa- 
tive of a different and of a hostile nation : "... tout 
cela pr6sente avec beaucoup d'elegance, assure a 
Touvrage des Principes, la preeminence sur les autres 

THE " PRINCIPIA." 1687 108 

productions de 1'esprit humain " extreme but not 
exaggerated praise. 

The " Principia " is not a compendium of knowledge 
reproducing the learning of the past with original 
touches here and there. It is one of the most 
consistently original books ever written. The funda- 
mental laws of mechanics are here formulated for the 
first time, the mathematical ideas required in the 
arguments are those invented by the author himself, 
the forces invoked to explain the motions considered 
are those arrived at by the author's own intuition, 
the phenomena explained had never been satisfactorily 
accounted for before, the problems initiated have since 
occupied the best minds of humanity for two centuries 
and a half, the results deduced have been the admira- 
tion of successive generations of astronomers and mathe- 
maticians and pervading the book there is a spirit of 
dignity and simplicity, a sanity of outlook, a soberness 
of expression, and a grandeur of conception, that place 
both the author and his work on an unequalled level 
of eminence. Immortals themselves, Halley and La- 
place could appraise at its true value genius superior 
to their own. 

It is quite impossible to convey an adequate impres- 
sion of Newton's achievements in the " Principia " in 
a brief space and in non-technical language. A mere 
enumeration of the topics discussed is sufficient to 
impress with wonder and admiration one so versed 
in the subjects of mechanics and astronomy as to 
appreciate the importance of these topics. First there 
is an introduction, in which, after some definitions and 
the consideration of the meaning of space and time, 
Newton formulates the three laws of motion that are 
still called by his name, with deductions and applica- 
tions of interest and significance. 

We have already stated how significant for the 
development of dynamical astronomy were the 


dynamical experiments of Galileo ; without them the 
whole subject was quite unapproachable. Newton 
therefore gives in the " Principia " a clear statement 
of the laws of motion deduced from these experiments. 
The first two laws have already been mentioned, 
namely, that the absence of force implies uniform 
motion in a straight line, while change of motion or 
acceleration is determined by force. A third law must 
now be added : its importance in connexion with our 
present subject is hardly ever explained adequately, 
whereas without it Newton's work would have been 
wofully incomplete. 

The third law of motion is the famous statement 
that action and reaction between two bodies are 
always equal and opposite. We can readily see the 
importance of this law in Newton's train of thought. 
Newton's use of the principles of dynamics was in 
itself a lesson in their clarification and of their sig- 

Astronomical progress from the flat earth to the 
spherical earth and from the fixed spherical earth to 
the- earth as a rotating and revolving planet, implied 
more than this bald statement seems to convey. 
The human intellect needs an anchorage in space and 
time as much as it needs one in its spiritual life. This 
was found in the flat earth. Man was banished from 
the flat earth and sent to wander in bewilderment 
round the surface of a sphere. Still, he had the 
centre of the earth, the fixed centre of all things. 
Copernijps completely banished man's intellectual 
anchorage from the earth and sent it to the sun. 
Humanity struggled against the decree of banishment, 
but finally and with a bad grace it submitted, and 
promptly appropriated the centre of the sun as the 
fixed point, the hub of the universe, the centre of all 
creation. Kepler's discovery of the more accurate 
paths of the planets left this state of affairs unchanged 

THE "PRINCIPIA," 1687 10T 

the sun remained enthroned in mighty splendour at 
the centre of the universe, directing his vassals, the 
planets, and their satellites. 

Meanwhile Galileo discovered the laws of dynamics. 
When we discuss motion, especially variations in 
motion, we necessarily look for a comparison point. 
When we say that a body is at rest we cannot mean 
anything else than that it is not changing its position 
relative to a set of bodies which we take to be the 
standard. Is the reader at rest while reading this 
page ? Is he reading this book in his house seated 
quietly near the fire or comfortably in bed ? He is 
clearly at rest yet he is being dragged round with 
the earth's diurnal rotation and with the earth's 
annual revolution. What then shall be our standard 
of rest in dynamics ? To which body are we to refer 
motions in order to decide whether they are uniform 
or varying, and what the variations are ? 

It is a remarkable feature of natural phenomena 
that in spite of their apparent complexity, Nature 
always contrives to make our researches into her 
secrets amenable to our limited intellectual powers. 
Galileo carried out his experiments on the earth he 
ignored the earth's motion completely. The effects of 
the earth's motion on his experiments were negligible, 
because the earth's angular rates of rotation and 
revolution are both so small as to produce no appreci- 
able effect on ordinary terrestrial dynamical phenomena. 
These and other considerations made it possible for 
Galileo to arrive at correct conclusions about the 
earth's gravity, and about the effects of forces on 
bodies. Would we even now be in possession of 
reasonable views on dynamics if the earth were a very 
small body, say ten miles in diameter, or if it rotated 
on its axis once in ten minutes, or revolved round 
the sun once in twenty-four hours ? The phenomena 
of solar and terrestrial gravitation would be so 


confounded together, as well as with variations in the 
earth's gravity itself, that no rhyme or reason could 
have been discovered in the subject by finite intel- 
ligences. Let us be grateful to a kindly Nature for 
presenting her problems to us step by step, and not 
confounding us with a too precipitate confrontation 
of all her complications. 

Galileo could take the earth as his "dynamical 
standard ; in fact, the surface of the earth wherever 
he happened to be was good enough for his purposes. 
This would of course be absurd in dealing with extra- 
terrestrial dynamics. People still take the sun as 
dynamical standard, and we often hear loose talk about 
the sun being fixed at the centre of the solar system. 
But Newton had to postulate universal gravitation, 
that all bodies attract one another the sun pulls the 
planets and the planets pull the sun, the earth pulls 
the moon and the moon pulls the earth ; it were there- 
fore ridiculous to imagine the sun " nailed down " 
and not yielding at all to the attractions of all the other 
bodies in the solar system. For this problem Newton 
used the third law of motion. Let the sun and earth 
attract one another, but let the force of attraction 
exerted by each on the other be the same, yet in 
opposite directions. The accelerations produced will 
be inversely as the masses, and it is at once seen that 
the point which divides the distance between the centre 
inversely as the masses will in fact have no accelera- 
tion at all ! A little mathematical reasoning enabled 
Newton to extend this to the whole solar system ; 
the centre of gravity of the whole solar system has no 

What about the so-called fixed stars ? Do they 
attract ? Why not ? Of course they do. Then there 
are external forces on the bodies of the solar system, 
and its centre of gravity has not zero acceleration. 
We have here once more an example of the benignity 

THE " PRINCIPIA," 1687 107 

of Nature towards human scientific research The 
stars are indeed so far off that Newton made no serious 
error in neglecting the accelerative effect of their 
gravitational pulls. He had no real knowledge of 
the distances of the stars, but the intuition of genius 
stood him in good stead. 

Newton thus took the centre of gravity of the solar 
system to have no acceleration. The logical thing 
would be to say that it has a uniform speed in a 
constant direction. But Newton had no means of 
discussing the motion of the solar system as a whole 
this came over a century later. He therefore took a 
deep plunge and as we shall see later he made the centre 
of gravity be at rest. It was left to the nineteenth 
century to correct this, and to the twentieth century 
to draw far-reaching conclusions from the correction. 

One of the most interesting features of the " Prin- 
cipia " is this continual provocation of thought on 
the part of the reader. The main theorems and pro- 
positions are given in clear, brief, crisp and conventional 
language. The implications of the theorems are dis- 
cussed in corollaries, and particularly in the " Scholia." 
A scholium is a general remark or conclusion that 
Newton often appends to some particularly important 
proposition and set of propositions. The scholia 
contain a vast amount of stimulating discussion, and 
they shed a large amount of light upon the whole 
subject, by means of the citation of authorities, 
experimental investigations and results, and any- 
thing else that helps to illuminate the matter in 

The main work is in the two books of the " De 
Motu Corporum " and in a third book on " De Mundi 
Systemate." Book I (the first part of " De Motu ") 
commences with a brief account of the principles of 
the method of fluxions the first printed statement 
of this discovery ever issued by Newton. We have 


already seen that Newton had written brief treatises 
on fluxions about twenty years before. His dis- 
coveries in this field were communicated in manuscript 
to several mathematicians, and some correspondence 
with Leibnitz had taken place as far back as 1676. 
Eight years later Leibnitz published in the " Acta 
Eruditorum " a mathematical journal edited by 
himself at Leipzig in Saxony an account of the 
differential calculus, essentially the same method as 
fluxions, but with a different and in fact more suitable 
notation, giving an oblique reference to Newton's 
work of a similar kind. Leibnitz developed the 
subject further in another paper two years later, 
1686. No doubt Newton read these papers and felt 
that the time had come when he should give to the 
world his own theory of fluxions. He accordingly 
incorporated in the " Principia " a section on this 
subject, in the form of eleven lemmas or preliminary 
propositions required for the sequel. The treatment 
is very brief, and even at this late hour twenty-one 
years after his developing the method the notation 
is not given ; this was not printed till six or seven 
years later in the works of John Wallis ! Meanwhile 
Leibnitz' method and notation were being used on 
the Continent with phenomenal success for solving 
difficult and important problems. 

After this preliminary, Newton attacks the motion 
of a body under an attraction directed to a fixed point. 
When the path is a conic section the force must bear a 
certain relation to the distance this is discovered, 
and then particularized for the case where the centre 
of attraction is at a focus of the conic, when the law 
is that of the inverse square of the distance. Detailed 
developments of this type of motion follow, and Newton 
examines the way in which any particular orbit is 
described, showing how to find the position at any 

THE " PRINCIPIA," 1687 109 

This would suffice for the discussion of the planetary 
motions in accordance with Kepler's third law. But 
Newton did not merely attribute gravitational pro- 
perties to the sun as acting on the planets or to the 
earth as acting on the moon. It soon became clear to 
him, especially on the basis of his third law of motion, 
that every heavenly body attracts every other heavenly 
body, that our earth attracts and is attracted by the 
moon, that the sun attracts and is attracted by the 
planets, that Jupiter attracts and is attracted by his 
satellites. It is a further instance of the encourage- 
ment that Nature gives to scientific discovery that the 
sun is so large compared to the planets, containing 
about a third of a million times as much matter as the 
earth, indeed about eight hundred times as much matter 
as all the planets put together, and further that the 
planets are very far apart. The result is that it is 
permissible in discussing the motion of any one planet 
to omit the pulls exerted upon it by the other bodies 
in the solar system, and to assume that it moves under 
the sun's influence alone. The same applies to a 
satellite. Satellites are usually so close to the planets 
round which they revolve, that even the sun's distur- 
bance can be neglected, at least as a first approximation. 
Again we might ask ourselves what progress in astron- 
omy would have been possible if, say, the planets had 
masses which were considerable fractions of the sun's 
mass, or if two planets came occasionally very close 
together, or if our moon were very much further away 
from the earth than it actually is. 

The problem of the sun and one planet, of a planet 
and one satellite, was the problem discussed by 
Newton primarily. But he had to go to a second 
approximation in order to explain a number of 
irregularities observed in the motion of the moon, 
and known for centuries. Newton's law of uni- 
versal gravitation suggested what had not yet been 


discovered, namely, that even Kepler's laws were only 
approximately correct. Happily, Kepler lived at a 
time when these mutual disturbances or perturbations 
of planets were not measurable instrumental accuracy 
had not risen to this level. He could therefore deduce 
the elliptic motion round a focus without being troubled 
by the occasionally quite considerable deviations there- 

In the case of the moon the disturbances were so great 
as to have been observable long before Tycho Brahe, 
Kepler and Newton. The moon thus presented an 
excellent means of testing not only the first rough 
results of Newton's theory, but also its more accurate 
consequences. The preparation for this is contained 
in the next section of Book I, where Newton discusses 
the effects of any law of force, the case of paths which 
are not closed, so that the moving body does not 
return to its original position exactly, as well as of 
oscillatory motions. 

A very important and fundamental theorem now 
follows. Newton was not content to attribute gravita- 
tion to the sun as a whole, or to any body like the 
earth or moon as a whole. He sought to discover the 
gravitational effect of any body on the basis of allowing 
each particle of the body to attract for itself, in which 
case, of course, it cannot be guessed off-hand what the 
total effect would be, even in such a simple case as a 
sphere the really important case in astronomy. In 
a singularly beautiful manner Newton proves that if 
the matter of a sphere is arranged symmetrically 
round the centre it produces at any outside point the 
same force as if all the mass of the sphere were con- 
centrated at the centre of the sphere. 

What was the use of this theorem ? Could not 
Newton say that this is the law which he postulates, 
since heavenly bodies are spheres ? Newton knew, 
however, that in this consideration of the attraction 

THE " PRINCIPIA," 1687 111 

produced by the separate particles of a body he had 
the key to many mysteries the flattened shape of 
the earth, precession, tides, etc. Some theorems on 
the attractions produced by non-spherical bodies 
follow, and Book I comes to an end with a somewhat 
irrelevant discussion of motions that refer to Newton's 
conception of light as due to tiny corpuscles moving 
with great speed this last piece of work is now entirely 
out of date and discarded. 

Book II of " De Motu Corporum " deals with the 
problem of motion in a medium of some kind which 
might produce a resistive effect to the motion. New- 
ton takes this resistance to be proportional first to 
the velocity, and then to the square of the velocity ; 
finally he takes the resistance to be in two parts, one 
proportional to the velocity and the other to the 
square of the velocity thus anticipating in remarkable 
manner modern ideas on air resistance in aeronautics. 
The results are then applied to motions under central 
attractions where resistance of this kind exists, and 
interesting results in the form of spiral motions de- 

This leads Newton to the consideration of fluids in 
general and their equilibrium under gravitational 
attractions a subject which has become of great 
importance in connexion with the discussion of the 
shapes of heavenly bodies. Since the pendulum is 
important in measuring the force of gravity at the 
earth's surface, Newton examines the motion of a 
pendulum in a resisting medium like air, and naturally 
proceeds to discuss the way in which the resistance 
depends upon the size and shape of the bob of the 
pendulum, upon the density of the medium, upon the 
velocity, etc. The study of wave motion in fluids comes 
next, and the velocity of propagation of such a wave 
is obtained by Newton, with obvious application to 
the propagation of sound through air. Experimental 


verification was attempted in that famous walk in 
the cloisters of Neville's Court at Trinity, where the 
modern don or modern undergraduate never fails to 
test the quadruple echo which Newton claims to have 
heard there. Experimenting in this walk Newton 
measured the velocity of sound roughly, with qualita- 
tive if not quantitative verification of his mathematics. 

One further point had to be settled before Newton 
could proceed to the application of his theory to the 
solar system. The Cartesian theory of vortices was 
then the accepted view of the cause of the motions of 
the planets. This theory had to be demolished first, 
and Newton disposed of it in a few simple propositions. 
He first shows that if the vortices exist and persist 
then they must be such that the fluid in each vortex 
rotates as a whole, as if it were one rigid body, with- 
out differential angular motions. It follows that the 
further a point is from the axis of the vortex, the 
faster it moves, so that the vortex theory gives velocities 
to the planets which are in complete contradiction to 
the observed velocities, the planets being known to 
move faster when nearer the sun and slower when 
farther away from the sun. " Hence the Vortex 
Theory is in complete conflict with astronomical facts, 
and so far from explaining celestial motions would tend 
to upset them/' 

The stage is now set for the final scene, the recon- 
struction of the phenomena of the solar system by 
means of the law of universal gravitation. Book III, 
" De Mundi Systemate," the book that Newton was 
for suppressing when worried about Hooke's claims to 
prior discovery, shows us Newton at the very pinnacle 
of his intellectual achievement. Here we see him as 
if he were a creator conjuring up before our charmed 
vision whirling and rotating planets and satellites, 
flowing and ebbing tides, erratic wanderings of 

THE " PRINCIPIA," 1687 113 

A brief preface in the form of " Hypotheses " 
contains two statements that throw a brilliant light upon 
the scientific character of Newton's thought. Right 
through the Middle Ages all thinkers differentiated 
somehow between earthly and celestial phenomena, 
postulating mystical causes and effects which bore 
little if any relation to ascertained facts. Newton 
broke with this most forcibly. " Like effects in nature 
are produced by like causes/' he asserted, " as breathing 
in man and in beast, the fall of stones in Europe and 
in America, the light of the kitchen fire and of the 
sun, the reflection of light on the earth and on the 
planets." Thus was humanity finally redeemed from 
the bondage of many centuries to belief in the per- 
fection of the heavenly, imperfection of the earthly, 
and all phenomena were reduced, or raised, to the 
same level of rational causality. 

It is interesting that Newton takes as his first proof 
of the inverse square law the fact that the periods and 
distances of the satellites of Jupiter and Saturn follow 
Kepler's third law, i.e. the squares of the periods are pro- 
portional to the cubes of the mean distances. Why 
does not Newton give the case of the moon first ? 
We have here another illustration, perhaps, of Newton's 
preference for the immediately visible, Anybody can 
verify the relationship between the periods and 
distances of the four large satellites of Jupiter not 
much observation is needed ; whereas the case of the 
planets round the sun needs careful measurement, 
and the case of the moon is a somewhat recondite 
application of dynamical principles, not well under- 
stood by many men in Newton's day. 

Having established the gravitation of Jupiter, Saturn, 
the sun and the earth, Newton then leads on to the grand 
generalization of the law of universal gravitation, the 
force between two bodies being proportional to the 
product of their masses, and inversely proportional 


to the square of the distance between them. He 
shows that no appreciable resistance is experienced 
by the planets so that their motions may be expected 
to go on indefinitely. He then determines the motion : 
the centre of gravity of the sun and all the planets 
is at rest a great improvement on the Copernican 
system in which the centre of the sun was taken to be 
at rest the sun never receding much from this point, 
while the planets move round the sun in ellipses, with 
a focus of each ellipse at the sun. 

Newton establishes the uniform rotations of the 
planets by reference to the moon's librations, already 
mentioned here, and then proceeds to discuss the shape 
that a planet should assume, using the knowledge of 
the apparent flattening of Jupiter at its poles, as told 
him by Cassini of Paris and Flamsteed of Greenwich. 
He proves that the rotation of a planet will cause such 
flattening, and discusses pendulum observations in 
the case of the earth to show that the variation in the 
earth's gravitation from place to place on its surface 
is explainable by this flattening. 

The flattening of the earth explains the precession 
of the equinoxes, a phenomenon known since the middle 
of the second century B.C., and completely misunder- 
stood till Newton gave it its natural explanation. 
Since the earth is not an exact sphere, the attractions 
exerted upon it by the sun and by the moon do not 
pass through the earth's centre, but meet the earth's 
axis at some little distance away from the centre. 
The effect in each case is to produce a turning effect, 
or moment, about an axis lying in the equatorial 
plane of the earth ; this gives a gyroscopic or top 
motion, in which the axis of the earth describes a 
cone in the heavens. This is one of the most beautiful 
deductions from Newton's theory that can be imagined, 
and the agreement quantitatively leaves little to be 

THE " PRINCIPIA," 1687 115 

Having shown in considerable detail that the 
irregularities observed in the motions of the moon and 
of the satellites of Jupiter and of Saturn (the only 
secondary bodies then known) can be explained by 



FlG. 8 

Pull of sun or moon on earth does not (owing to flattening of the earth) pass 
through its centre, as shown here. A torque is produced about an axis through 
the earth's centre perpendicular to the plane of the paper. This causes the earth's 
axis to " precess," like a top, in the reverse sense to the earth's own rotation. 

gravitation as due to the perturbative effect of the sun, 
Newton proceeds to the question of tides. He at once 
attributes the tides to the differential gravitative effects 
of the sun and moon. If we consider the earth and 
the moon, the former containing on its surface a flowing 



substance like water, we see that the attraction 
produced by the moon on unit mass of the water on the 
side of the earth away from the moon must be less than 
on unit mass on the side towards the moon, while on the 
earth itself the attraction corresponds to the total mass 
of the earth concentrated at the centre of the earth, 
and thus per unit mass produces effects lying inter- 
mediate between those on the further and nearer 
waters. The result is that the nearer waters are 
dragged towards the moon more than the earth as a 

FIG. 9 


Gravitational pulls of Sun and Moon on Tides due to sun and moon respectively. 
Earth, and on waters on near side and on 
far side of Earth. 

whole, and the further waters are dragged towards 
the moon less than the earth as a whole. The waters 
are thus heaped up on the two sides of the earth, 
towards the moon and away from the moon. 

The same applies to the sun. But the moon is so 
near that its tidal effect is greater than that of the sun ; 
hence the tides follow the moon as a whole. Hence, 
also, we get the very high tides at new and full moon, 
when the sun and moon reinforce one another's tidal 

THE " PRINCIPIA," 1687 117 

effects, and low tides at the quarters, when the sun 
and moon tend to neutralize one another's tidal effects. 
Finally we get a rational and beautiful treatment of 
comets. Newton's knowledge of comets was some- 
what scanty when he discussed them with Flamsteed 
several years before he wrote this theory. But in the 
" De Mundi," he produces a remarkable account of 
the subject. He proves that comets must move in 




FlG. 10 

Long ellipse with one focus at the centre of the sun. 

interplanetary space and shows that they also move in 
conies about a focus. Kepler's ellipses were one type 
of conic the cometary paths ate another type, 
vindicating wonderfully the generality of Newton's 
gravitational ideas. Newton then reverts to the 
parabola as an approximation to a long cometary 
ellipse, and discusses how to find the approximate 
parabolic path of a comet from three observations of 
its position as seen from the earth a result of funda- 
mental importance, since by its means one can deduce 
the future path of a comet quickly after its first 
appearance, so as to facilitate observation and a more 
accurate determination of its path subsequently. 


There is much in the " Principia " to which we have 
not referred and which is of great importance in the 
theory of the heavenly motions . We have talked about 
the masses of the planets and of the sun. How can 
we find these masses ? - Nothing is simpler when we 
have once grasped the fundamental idea of gravitation. 
If a planet has a satellite, then by the motion of the 
satellite we can calculate the gravitative effect of the 
planet at the distance of the satellite. But we have 
the gravitative effect of the sun for all sorts of dis- 
tances. By comparison we get the ratio of the gravita- 
tive effects of the sun and of the planet for the same 
distance, and this is the ratio of their masses. In this 
way Newton could find the ratio of the mass of the sun 
to that of the earth or of Jupiter. Now we can find 
this ratio for all the planets in this way, except Mercury 
and Venus which seem to have no moons. 

No limit can indeed be foreseen to the developments 
consequent upon Newton's work. The " Principia " 
is not an ordinary book which plays its part in the 
progress of knowledge and then disappears. Its 
theorems and methods, principles and laws, are pro- 
nouncements that humanity has studied for genera- 
tions. Over and over again the greatest triumphs 
of human thought have been achieved as the direct 
consequence of Newton's genius. The exact working 
out of the motions of the bodies in the solar system at 
the hands of Laplace, Lagrange and their successors 
has introduced into astronomical prediction such a 
degree of precision that popular concern is aroused 
when an eclipse takes place a couple of seconds earlier 
or later than the time calculated in advance, and 
messages are cabled round the world to announce this 
fact. The slight differences between the observed 
motion of Uranus and that calculated on the basis 
of the sun's attraction and the perturbations due to 
the known planets, led to the discovery on paper by 

THE " PRINCIPIA," 1687 119 

mathematical calculation of the till then unknown 
planet Neptune. The difference between the motion 
of Mercury and that deduced from theory has been one 
of the main planks in Einstein's platform. And what 
is perhaps the outstanding event in the science of our 
own generation the theory of relativity is a wonder- 
ful vindication of the sagacity of the originator of 
universal gravitation, for it is the universality of 
gravitation that is the chief argument in Einstein's 
view, and the universality of gravitation is the dis- 
tinctive characteristic of Newton's conception of this 

But one of the most historic vindications of Newton's 
genius was coupled with that of none other than his 
friend and admirer Halley. Man is always impressed 
with the power of foretelling events yet to come, and 
Halley was able to present to the world a remarkable 
piece of prophecy, the fulfilment of which was left 
to the generations that came after him and made him 
one of the immortals of astronomy. 

A great comet had appeared in 1682, and Halley 
had observed it carefully, deducing its path when near 
the sun. When Newton published the " Principia " 
and demonstrated that long elliptic paths with a focus 
at the sun are possible, he concluded that what appears 
to be a parabolic path of a comet may really be a long 
elliptic path, and suggested that the periodic time of a 
comet moving in a long ellipse could be ascertained by 
its return after a long interval of time. But a comet 
becomes visible to us only when it is near the sun, 
whose effect is to eject matter from the comet ary 
nucleus in the form of one or more tails. Thus a 
comet is invisible except for a very short time when 
it is near the sun, and a comet could not be traced 
all round its elliptic orbit in order to verify Newton's 

The sagacity of Halley came to Newton's help. 


Halley set himself to examine all reliable observations 
of comets that had appeared in the past, and 
where sufficient material existed he calculated the 
parabolic path which Newton took to be the 
first approximation. He discovered that in the year 
1607 a comet had been observed whose approximate 
parabolic path was very nearly identical with that of 
1682. This was interesting as a coincidence, perhaps. 
But Halley found that in the year 1531 a comet had 
been observed whose approximate parabolic path was 
also nearly identical with that of 1682 further, the 
interval 1531-1607 is nearly the same as the interval 
1607-1682. Halley became convinced that this was 
not a cometary accident or coincidence, but rather a 
cometary habit, and concluded that he had indeed 
discovered a periodic comet, the existence of which 
was suggested by Newton. Any deviations from exact 
identity of the calculated parabolas, and any inequality 
between the two intervals, Halley attributed to 
planetary perturbations. 

Newton encouraged Halley in this view, and in 
1705 Halley announced that the comet he had observed 
in 1682 would reappear after suffering severe per- 
turbation owing to a very near approach to Jupiter 
about the end of 1758 or the beginning of 1759. Halley 
had looked back into the centuries and observed the 
similarities of the cometary paths of 1531, 1607 and 
1682 ; he looked forward, with the aid of Newton, into 
generations to come and saw his comet wending its 
long and lonely way, past the orbit of the earth, past 
the orbit of Mars, past Jupiter, past Saturn, deeper 
and deeper into space. Halley and Newton grew older 
and older. Newton passed away and Halley was left 
to continue alone the dynamical watch of the comet. 
He rewrote his prediction, and, feeling that he would 
never see the year of the comet's return, expressed 
the hope that if the comet did come back as predicted 

THE " PRINCIPIA," 1687 121 

" impartial posterity will not refuse to acknowledge 
that this was first discovered by an Englishman. 1 ' 

Within a month of the time given by calculations 
based upon Newton's laws the comet reappeared. 
Halley was dead, but grateful posterity will forget 
neither Halley's personality nor his nationality. 
Halley's Comet reappeared in 1835 and in 1910, in 
better and better agreement with calculated time and 
place a lasting monument (not permanent since 
comets disintegrate, and Halley's Comet is believed 
by some to be showing signs of decay already) to the 
memory of Newton and Halley. It is exceedingly 
appropriate that Halley's memory should have thus 
become linked with that of the man whom he admired 
so selflessly and encouraged with such devotion. 

Such are the contents of the " Principia " as issued 
in 1687, written by the man driven out of his court 
by Jeffreys and admonished to mend his ways, and 
printed at the personal expense and risk of the man 
who could best appreciate its contents. 


Has matter more than motion ? Has it thought, 
Judgment and genius ? Has it framed such laws, 
Which, but to guess, a Newton made immortal ? 

EDWARD YOUNG : " On the Being of a God " 

EVERY new idea has to overcome prejudice 
and mental inertia. The publication of the 
" Principia " was a turning point in the in- 
tellectual history of mankind ; yet Newton came on 
the scene when Descartes' vortex theory had become 
well entrenched, enjoying the prestige associated with 
the immortal name of this philosopher and mathe- 
matician. On the Continent, in fact, Newton's theory 
made little progress for some time. The supposed 
suggestion of action at a distance, without any hypo- 
thesis as to how the action was propagated in the 
intervening space, caused considerable opposition on 
the part of Leibnitz and others, especially when 
personal jealousies confused^he issue. It will already 
be clear to the reader that ^ewton was the last man 
in the world to postulate non-physical or anti-physical 
conceptions ; he did indeed make an attempt at a 
physical explanation of gravitation based upon the 
jetherji But this effort produced nothing really useful, 
and more than two centuries had to elapse before a 
satisfactory view of gravitation began to emerge. 

Things were better in England, where Newton's 
work found ready approval among those few whose 
opinions were worthy of consideration. Within three 



years of the publication of the " Principia " its 
contents were taught at Cambridge, St. Andrews and 
Edinburgh, while Oxford followed suit before very 
long. The " Principia " helped to establish mathe- 
matical studies on a firm basis, especially at Cambridge. 
Non-mathematical thinkers took special pains to study 
the physical portions of the book, and the influence of 
Newton's ideas spread quickly among the best minds 
of the day. The " Principia " sold quickly, and one 
hopes that Halley did not lose on his generous trans- 
action. Copies of the first edition became scarce, and 
people paid four or five times the original cost for a 
copy. One case is known of a Scotsman who wrote out 
the whole book by hand, as he could not get a copy 
at a reasonable price. 

Following Halley's advice Newton took a rest from 
scientific work. In November, 1688, William of 
Orange landed at Torbay and marched upon London. 
James II fled the country and William was invited to 
share the throne with his wife, James 1 daughter, 
Mary II. In January, 1689, the so-called Convention 
Parliament was summoned to Westminster, and, as 
Macaulay says : " Among the crowd of silent members 
appeared the majestic forehead and pensive face of 
Isaac Newton ... he sate there, in his modest great- 
ness, the unobtrusive but unflinching friend of civil 
and religious freedom." Parliament did not hear 
Newton's voice in debate during the thirteen months 
that he served as M.P. for Cambridge University 
, till the dissolution in February, 1690 yet Newton's 
presence was not unfelt. He was a keen supporter of 
the new royal house and a Whig in politics, being a 
strong believer in religious toleration, and a stout 
opponent of all forms of oppression in particular 
of the oppression, religious and otherwise, practised 
by the Stuarts. He did much to make and keep 
Cambridge loyal to King William and Queen Mary. 


Newton's presence in London served to accentuate 
the unsatisfactory nature of his own personal position. 
He was nearly fifty years of age, and he had spent all 
his manhood days in the most unremitting scientific 
toil. No recognition of a tangible nature had come 
to him. He was still college fellow and university 
professor, conscious of a harrowing poverty, which 
narrowed his existence and prevented him from 
satisfying the needs of his relations and other depen- 
dents, and which had necessitated his acceptance of 
Halley's offer to shoulder the financial responsibility 
involved in printing the " Principia." 

Locke, Pepys and other friends of Newton who 
occupied prominent positions in public life tried to 
secure for him some public post worthy of his great- 
ness. In particular, Charles Montague, an intimate 
friend of Newton's and a fellow-member of the Con- 
vention Parliament, who was rising quickly in the 
political firmament, did all he could for him. But the 
great men of the day were too busy to bother about a 
mathematician whose work they could not under- 
stand. When the post of Provost (or Head) of King's 
College, Cambridge, fell vacant, Newton was nomi- 
nated, but ultimately failed to secure appointment 
because he was neither a Fellow of King's nor in 
priest's orders. The dissolution saw Newton back in 
Cambridge, resuming his bachelor life in a college cell. 

Meanwhile other things had happened to depress 
Newton. During the year of his membership of the 
House of Commons his mother, Mrs. Smith, became 
seriously ill, and Newton left everything to minister 
to her. He was a skilful nurse ; he sat up with his 
mother whole nights, and did everything in his power 
to lighten her sufferings. She died without having 
enjoyed the satisfaction of seeing her son Isaac receive 
the token of his nation's gratitude that was his 


Did his mother's death turn Newton's attention to 
theology ? As early as 1690 his interest in theological 
discussion began to manifest itself and was encouraged 
by others. He corresponded with various people 
about gravitation, and drew up for John Wallis in 
1692 a few propositions on fluxions, which were 
printed in the second volume of Wallis 1 works ; he 
corresponded with Leibnitz about his mathematical 
work ; he gave free rein to his lifelong interest in 
alchemy and studied many old and contemporary 
books on this subject ; he interested himself in a 
method due to Boyle for making gold out of mercury ; 
but one of the most important of Newton's productions 
during the period 1690-1693 was in the domain of 

In 1690 Newton wrote, but did not publish, a 
discussion of " Two Notable Corruptions of the 
Scriptures, in a Letter to a Friend." These referred to 
I John v, 7, and i Tim. iii, 16, and Newton claimed 
that the trinitarian interpretations of these passages 
were not justified by the correct original text. It is 
difficult to say whether Newton did or did not believe 
in the Trinity ; at any rate, it is clear that he did not 
accept all the tenets of the prevailing Church unques- 
tioningly, and was as independent in theological belief 
as in scientific investigation. Newton also wrote then 
and later on the Prophecies of Daniel, on the Apocalypse 
of St. John, and about many other religious topics. 
But the most famous of his theological writings are 
his letters to Bentley. 

Richard Bentley was a brilliant young scholar who 
afterwards became Master of Trinity. He was inter- 
ested in gravitation, and Newton gave him advice on 
the preliminary reading in mathematics needed in 
order to be able to follow the " Principia." In 
December, 1691, the famous Robert Boyle died and 
left some money to endow a lectureship in the interests 


of Christian orthodoxy. Bentley was appointed the 
first lecturer under the bequest, and he decided to 
devote two out of the eight lectures to a consideration 
of divine providence as evidenced by the physical 
universe. But he encountered some difficulties and 
applied to Newton for help. Newton replied in four 
letters, written between December, 1692, and February, 

Bentley's chief difficulty was the argument used 
by the Roman poet Lucretius, who had claimed that 
there is no need for postulating a divine creation, 
since matter evenly scattered throughout space, and 
endowed with the power of gravity, would form the 
universe as we know it. Newton replied that matter 
in a state of diffusion could not, if left to itself, and 
without the aid of Divine will and design, produce 
differently constituted bodies like the bright sun and 
the dark planets, and could not endow the planets with 
their characteristic nearly circular motions round the 
sun. Plato's idea that the planets originated very far 
away and then fell inwards till they reached their 
present orbits, was proved by Newton to be incon- 
sistent with the law of gravitation, since it would 
imply a sudden halving of the sun's attractive power 
when the planets assumed their orbital motions. 
Nowadays we would not take it as obvious that 
diffused matter, or nebula, will not explain the forma- 
tion of the solar system a nebular hypothesis has in 
fact become associated with such names as Kant, 
Herschel and Laplace. 

Meanwhile Newton's bachelor habits began to tell 
upon his health. He must have had an excellent con- 
stitution, since he enjoyed a long life in spite of his 
many years of irregular and insufficient sleep, and 
negligence as regards food and other bodily comforts. 
He became physically unwell and suffered from 
nervous irritability. He began to brood over the 


injustice done him, which his experience as a member 
of the House of Commons had made him feel most 
keenly. Public offices of honour and of profit were 
being bestowed upon the deserving and the undeserv- 
ing, men whose merits were incomparably lower than 
his own were playing a prominent role in the life of 
England ; while he saw no prospect for himself but 
the obscure and desolate life of the college recluse. 
Always difficult in personal relationships, Newton did 
not hesitate to charge his friends with being false to 
him, and wrote some silly letters to this effect. 

Newton's behaviour and unhappiness, aggravated as 
he himself testified " by sleeping too often by my 
fire [1692] ... so that when I wrote to you [Locke] 
I had not slept an hour a night for a fortnight together, 
and for five days together not a wink/' alarmed his 
friends very much. Highly coloured rumours were 
spread about his health. On the Continent, where 
Newton's work in optics had made a considerable 
impression, and his gravitational work was slowly 
penetrating, rumours were spread that he had become 
insane, and an interesting story was told to account for 
it. It was said that a little dog called Diamond had 
caused the loss by fire of Newton's laboratory, together 
with a manuscript containing the results of many 
years' labours. To add verisimilitude to the narrative 
the story went on to say that the meek and mild 
Newton " rebuked the author of it with an exclama- 
tion, ' O Diamond ! Diamond ! thou little knowest 
the mischief done ! ' without adding a single stripe." 
We have already seen that Newton did not keep any 
domestic animals. The fire, of which so much was 
made, and which produced only little damage, took 
place much earlier, before Newton had even begun to 
write the " Principia." 

In 1691 Newton resumed his work on the motions 
of the moon. This was a most difficult subject lunar 


theory is even now the most difficult branch of 
nervous dynamical astronomy and no doubt Newton's 
excitability was aggravated by these head-racking 
studies. He desired to get the best possible observa- 
tions of the moon in order to verify the results of his 
mathematical inquiries, and tried to get into touch 
with the Astronomer Royal, Flamsteed. But it was 
not till 1694 that really useful information was forth- 
coming, and Newton spent much of his time on 
his favourite chemical experiments. When Flamsteed 
was ready a correspondence ensued between him and 
Newton which lasted nearly two years. Flamsteed 
gave Newton observations of the moon, as well as the 
values he had deduced for the refraction produced by 
the air a matter of the greatest importance in con- 
nexion with the observations of the exact positions 
of heavenly bodies, since the apparent positions are 
always affected by the bending of the light rays in 
coming from outside the atmosphere into the atmo- 
sphere of the earth before reaching our eyes or our 
telescopes. Newton was able to make considerable 
progress with the theory of both subjects the moon 
and refraction and was very grateful indeed. Yet 
personal unpleasantness intervened for which Newton 
himself must bear a portion of the blame. 

Flamsteed was a very peculiar person, a permanent 
invalid who was never free from headaches and other 
more serious physical affections : he was not treated 
at all generously as Astronomer Royal, and had to 
pay his way by acting as a vicar at the same time as 
doing his astronomical work. He was a religious man 
and had an antipathy to Halley who was not very 
orthodox in his belief, and who had offended Flamsteed 
in astronomical matters. Newton was a very kind 
man, but he had gone through considerable physical 
suffering and had become impatient and excitable. 
He always became irritable in personal matters : in 


the words of his friend Locke : " Newton was a nice * 
man to deal with, and a little too apt to raise in him- 
self suspicions where there is no ground/' Further, 
Newton was a particular friend of Halley's who had 
done so much for him. 

This triangle led to difficulties and many hard words 
were said between Newton and Flamsteed, with Halley 
as the provocation. It is sometimes not uninteresting 
to note the pettinesses of the great a link is thus 
forged between more humble mortals and the men of 
transcendent genius, who would otherwise lose all 
semblance of frail humanity. 

While Newton was thus betraying his human weak- 
nesses against the greater weaknesses of Flamsteed, a 
complete change in his life and fortunes was preparing 
for him. His friend Charles Montague had not been 
false to him, but had used the first available oppor- 
tunity to give Newton evidence of his friendship, and 
at the same time save the reputation of England in 
regard to her treatment of the greatest Englishman of 
the day. Newton was busy with chemical experiments 
once again, and the call that now came to him was 
one in which he could exercise to the full his lifelong 
interest in metals and alloys. 

* Not in the modern sense, but in the Shakespearean sense of 
" fussy," " difficile:' 





" Thy silver is become dross." 

Isaiah, i, 22 

NEWTON had spent thirty-one years as a college 
graduate and fellow and university professor. 
This was just half of his adult years ; he had 
thirty-one years more to live, and these he spent in 
the midst of the public affairs of the nation and as 
the doyen of British science. 

From the time of Queen Elizabeth England had had 
a coinage based upon bimetallism both gold and 
silver were legal tender. But the silver coinage had 
become terribly debased by the use of bad and cheap 
alloys as well as by the prevalent habit of clipping 
the coins. Things were in a very bad state, even to 
the extent of English silver being refused by the Bank 
of Amsterdam the then financial centre of Europe. 
Such silver coins to the nominal value of five and a 
half million pounds sterling were in circulation, the 
actual value being less than eighty per cent of the 
nominal value. 

In 1694 Charles Montague was appointed Chancellor 
of the Exchequer, and he decided to restore the silver 
coinage to its full value. He had conferences with 
various people, including Newton, on the matter. 
The House of Lords proposed to cancel all such coins 
from some given date, so that the sufferers would be 



the poorest and those least able to bear it. The House 
of Commons decided, however, that the nation had to 
bear the loss, and resolved to issue new and full- valued 
coins in exchange for the old ones. A vast amount 
of work thus fell to the Royal Mint. 

Montague was an intimate friend of Newton's and 
President of the Royal Society. He therefore realized 
that he had in him the right man for carrying through 
this difficult project. The Wardenship of the Mint in 
London became vacant early in 1696, and on March 
i gth of that year Montague wrote to Newton, informing 
him that the King had appointed him to this post. 
" The office is the most proper for you. . . . Tis 
worth five or six hundred pounds per annum, and has 
not too much business to require more attendance 
than you may spare. I desire you will come up as 
soon as you can. ... I believe you may have a 
lodging near me." Newton accepted the post, and 
took over his new functions without delay. 

Although the Wardenship of the Mint had become 
a sinecure and incumbents hardly ever " condescended 
to come near the Tower," Newton took his new duties 
very seriously. Hard work was necessary, as the 
debased silver was causing much suffering and foment- 
ing popular dissatisfaction. " The ability, the industry 
and the strict uprightness of the great philosopher," 
says Macaulay, " speedily produced a complete revolu- 
tion throughout the department which was under his 
direction." " Well had it been for the publick, had 
he acted a few years sooner in that situation," said 
one who had business with Newton and could appreci- 
ate his merits at first hand. 

For three years Newton laboured in the nation's 
cause, and in 1699 the recoinage was complete. " Till 
the great work was completely done, he resisted firmly, 
and almost angrily, every attempt that was made by 
men of science, here or on the Continent, to draw him 


away from his official duties." Instead of producing 
fifteen thousand pounds' worth of silver per week, 
Montague and Newton had been able to increase the 
yield to one hundred and twenty thousand pounds' 
worth per week. They had to withstand all kinds of 
opposition,^ and underhand attempts at bribery and 
corruption-^ even open rebellion was threatened in the 
country. But a gratified nation recognized its bene- 
factors at last. In 1699 Newton was appointed 
Master of the Mint, a high office worth between twelve 
hundred and fifteen hundred pounds per annum 
which he held for the remainder of his life. 

Newton enjoyed his new circumstances for one 
reason in particular. He was always careless about 
money. Although scrupulously exact in all business 
matters, he sometimes suffered great losses by fraud 
or theft and bore them philosophically. But he took 
a great delight in giving money away lavishly. He 
was always ready to give, believing that a man should 
give during his lifetime and not wait till he is dead. 
Newton helped his many relatives, both on the paternal 
and on the maternal side : he was particularly kind 
to his stepsisters and stepbrother and to their families. 
Mary Smith got a permanent allowance from him. 
But it was a daughter of Hannah the younger sister 
who enjoyed Newton's special favour, and played 
a prominent part in his private life. 

Hannah Smith had married Robert Barton of 
Brigstock, Northamptonshire. In 1679 a daughter 
was born, called Catherine. She was a very clever 
girl and showed signs of becoming a great beauty. 
When Newton went to live in London, Catherine 
joined him and kept house for him for many years. 
Newton had no official residence at the Mint, although 
he apparently lived there in bachelor fashion at first. 
In 1697 he took a house in Jermyn Street (also written 
German Street), a street running parallel to Piccadilly, 


and connecting Regent Street and St. James Street. 
He had much entertaining to do, and naturally a 
beautiful and accomplished young lady, famous for 
her conversational powers and ready wit, was just the 
person to help Newton with his social duties. 

There is a tendency to regard Newton's transfer to 
London as a loss to science and as a confession on the 
part of the British people that the only way to reward 
scientific genius in one of its citizens is to make him 
relinquish his scientific work altogether since no 
posts exist in the academic sphere that are worth 
having, and that may be awarded as prizes for merit 
of the highest order. Much may be said even to-day 
about the inadequacy of the returns in academic life 
in Newton's days they were absurdly inadequate 
but it must be pointed out that in Newton's case any 
academic reward would by its very nature have been 
unsuitable. He was not exhausted scientifically, but he 
had made such stupendous scientific discoveries that 
he could not hope to improve on them. His place was 
no longer in a college or in a laboratory, but rather in 
the forefront of his nation's science, putting at the 
disposal of his people and of humanity his unique gifts 
as a worker and as a thinker. 

fFjom 1665 to 1696 Newton was essentially a scientific 
researcher, and laboured to unravel the laws of nature. 
For an equal period, 1696 to 1727, Newton was the 
servant of his nation and the foremost representative 
of British learning^ No greater mathematician, physi- 
cist and astronomer, combined in one person, ever 
existed, no greater Master and Warden of the Mint 
ever existed, and no more noble figure could be 
imagined to act as the presiding genius over British 
science. Newton's place was in Cambridge for the 
first half of his adult life, his place was in London 
for the second half of his adult life, when he had 
performed his scientific mission to mankind, and 


had become a figure of national and international 

Although Newton desired to devote himself exclu- 
sively to the important task that he had in hand at 
the Mint he could not escape being interested in the 
scientific problems of the day. He was consulted about 
the mathematical syllabus at Christ's Hospital, and 
gave excellent advice. He showed his great mathe- 
matical ability by solving in a few hours two problems 
that the celebrated John Bernoulli put as a challenge 
to the greatest mathematicians of the world. One of 
these problems had its origin in optical theory, and 
deserves mention since it contains the germ of an idea 
that has played a fundamental part in dynamical 
theory of the last hundred years. The problem was : 
Given two points A, B such that the straight line 
joining them is neither horizontal nor vertical, to find 
how the curve joining them must be drawn, so that if 
d particle starts from the top end and falls along the 
curve under gravity it shall reach the lower end in the 
least possible time. Newton showed that the curve 
required is a cycloid, or the path described by a point 
on the rim of a wheel while the wheel itself rolls along 
the flat ground. Such a curve is called a brachisto- 
chrone. The idea underlying the problem is that of 
the calculus of variations, and the suggestion that 
something in nature, say, a length or a time or an 
energy, is a maximum or minimum has become one of 
the most fertile methods of dynamical and general 
physical development. 

The work on the motions of the moon lay neglected 
for a couple of years, but at the end of 1698 Newton 
resumed it, once more in conjunction with Flamsteed, 
and once more with considerable unpleasantness in 
their personal relationships. In 1699, after declining 
an offer of a considerable pension from the French 
king Newton not only disliked gifts to himself, but 


he was also a very loyal Whig, " the glory of the Whig 
party/ 1 as Macaulay calls him he was elected a 
foreign associate of the French Academy, together with 
the most celebrated scientists of the day Leibnitz, 
James and John Bernoulli, and Roemer. 

In 1699 Newton decided that he could not continue 
as Lucasian professor, and appointed a deputy in that 
remarkable mathematician and theologian, William 
Whiston, the translator of Josephus. Whiston was 
very unorthodox in religious belief, but with Newton's 
help he was elected Lucasian professor, when in 1701 
Newton finally resigned his chair and his Trinity 
fellowship. As a matter of fact, Whiston was expelled 
from Cambridge in 1710 for his heterodox views. 

Newton still had a bond of union with Cambridge. 
In November, 1701, he was once more elected M.P. 
for Cambridge University, and sat till the dissolution 
in July, 1702, after the death of King William III, and 
the succession to the throne of Queen Anne. Newton 
did not seek re-election for some years. 

In scientific matters Newton's activity was uninter- 
rupted. In 1699 he drew up a scheme for a reformed 
calendar, with quite revolutionary suggestions, based 
upon an ingenious attempt to correlate the calendar 
with the actual equinoxes and solstices. In 1700 
Newton sent to Halley a description of an instrument 
he had invented for measuring the angle subtended at 
the eye by two inaccessible points. The instrument 
was, in fact, the sextant, so important in navigation 
and surveying: but nobody realized its value, -and 
John Hadley reinvented it in 1730 several years after 
Newton's death. rTnji7oi Newton published a paper 
on scales of temperature, incorporating two discoveries 
of great importance. The first was his law of cooling, 
which is that the rate of cooling at any moment of a 
warm body is proportional to the difference between 
the temperature of the body and of the surrounding 


medium, say, air. The second was that while a body 
is melting or evaporating its temperature remains 
constant. Both discoveries play important roles in 
modern physics?) 

Newton's standing in the world of science was 
unchallenged. The great Leibnitz said of him in 1701 
that his work in mathematics was worth more than 
all that had been done before him. This was an 
exaggeration, perhaps, and Leibnitz* relations to 
Newton later on did not suggest such a pitch of admira- 
tion. In England there was no doubt about Newton's 
scientific stature. The Royal Society was the estab-^ 
lished and recognized repository of all that was best 
in English science, and the post of President carried 
with it the status of pre-eminence in the world of 
knowledge. In November, 1703, Newton was elected 
President of the Royal Society. He was at last in the 
position, as it were, preordained for him. Most gifted 
of all Englishmen, supreme in knowledge and discovery, 
standing at the summit of happy achievement, and 
enjoying universal approbation and renown, Isaac 
Newton had risen from the obscurity of a county 
hamlet to be the glory of his nation and a blessing 
to mankind. 


Honour is not repugnant to reason, but may arise therefrom. 

Baruch Spinoza : " Ethics " 

NEWTON had become a prominent national 
figure. He moved in the best society and lived 
in considerable style. He employed many 
servants, kept a carriage, and entertained hospitably 
and well. His salary was more than he needed and 
he was able to exercise his charitable propensities to 
the full. He was ever ready to support the 
scholar, and he showed special favour to men in 
whom he discerned mathematical ability of a high 

The friendship that Newton enjoyed with the House 
of Orange was cemented in various ways. When King 
William III died in 1702 he was succeeded by his 
sister-in-law, Anne, the daughter of ex-King James II. 
Her husband was the good-natured Prince George of 
Denmark, who was elected to the Royal Society. As 
President, Newton came into contact with the Prince 
Consort and encouraged him in his design to do some- 
thing tangible for science. Prince George offered to 
pay the cost of printing Flamsteed's observations, 
including his star catalogue, and asked Newton, 
together with Wren and several other fellows of the 
society, to act as referees in the matter, and to decide 
which observations were to be printed and the order 
in which they were to be arranged. By the beginning 



of 1705 the referees had reported and the work of 
printing could begin. 

Queen Anne became interested in these matters, too, 
and learnt to see in Newton the man of highest genius 
in her land. On April 16, 1705, she visited Cambridge 
and held a court at Trinity Lodge . She took advantage 
of the occasion to confer upon Newton the dignity of 

Yet royal favour carried disappointment in its train. 
Parliament had just been dissolved. In the new 
elections Newton was prevailed upon by his Cambridge 
friends to offer himself for election once more. But 
the Tories were in the ascendant, and Newton suffered 
ignominious defeat only a month after he had been 
dubbed a knight. With four candidates in the field 
he was returned bottom of the poll. Newton never 
sought parliamentary honours again no real loss to 
the nation, since he was not cut out for parliamentary 
life or for a political career. He had always been shy 
of public discussion, even in matters scientific, and he 
never bore with a good grace criticism and opposition. 

Of Newton's private life we do not know much. He 
seems to have had close friends in other than royal 
circles, too, and he is credited with having written a 
very oblique sort of proposal of marriage to a Lady 
Norris a much-married lady who had survived three 
husbands. If the proposal was a reality it had no 
serious sequel. Newton was then sixty-three years of 
age, and he remained a bachelor to the end of his days. 
His niece Catherine continued to keep house for him 
till she married. 

The most important events in the remainder of 
Newton's life were of a scientific nature. Two im- 
portant works by nim were published soon after 
his elevation to the Presidency of the Royal Society. 
The first was on " Optics," and contained a connected 
account of all Newton's labours in this subject. The 


manuscript was ready for several years, but Newton 
did not wish to have it printed while Hooke lived, as 
he did not desire to have any further unpleasantness 
with him. Hooke died in 1703 and Newton's " Optics " 
was published in 1704. 

Unlike the " Principia," the " Optics " was published 
in English : a Latin edition appeared in 1706. The 
book was a great success : it enjoyed widespread 
approval, and several editions both in English and in 
Latin were printed within a comparatively few years. 
As is to be expected, the book deals with the composite 
nature of white light and with the cause of colour in 
bodies, with reflection and refraction upon the basis 
of Newton's corpuscular view of light, with colours in 
thin films and the theory of fits of preference for 
reflection and for refraction, with diffraction (called 
inflection), with the rainbow, with halos, etc. But 
in the first edition of the " Optics " two mathematical 
treatises, quite irrelevant to the main purpose of the 
book, were added. One was on " Quadratures of 
Curves," or really the theory of fluxions as used in 
finding areas enclosed by curves : the second was an 
account of seventy-two curves of the third order, so- 
called cubic curves. If the inclusion of the first paper 
was expected to make clear Newton's position as the 
inventor of fluxions, then the effect produced was the 
very reverse. In the review of the " Optics " in 
Leibnitz' organ, the " Acta Eruditorum," written by 
Leibnitz himself, but not signed, it was quite broadly 
hinted that Newton had simply taken Leibnitz' 
published work on the calculus, and rewritten it in 
the fluxionary notation ! 

Newton lectured on algebra while Lucasian professor, 
but he had not published his notes on the subject he 
was never anxious to display his pure mathematics, 
which he looked upon as a tool for physics and astro- 
nomy. William Whiston had attended these lectures 


in 1685 and so possessed them in manuscript : he had 
them printed in 1707. The book is in Latin and is called 
" Universal Arithmetic/' This book, too, was received 
with great approval both in England and on the 
Continent. An English translation appeared soon, 
while a second edition was issued within five years of 
the first. 

Meanwhile, the printing of Flamsteed's observations 
went on under Newton's supervision. A first volume was 
published in 1707, but the death of the Prince Consort 
in 1708, and Flamsteed's own dilatoriness, caused 
a delay of several years in the publication of the 
remainder. Newton and Flamsteed fell out over this 
again and again. The way in which Flamsteed carried 
on his work at the Royal Observatory was not con- 
sidered satisfactory, and finally the Royal Society asked 
the Queen to place the Observatory under some 
responsible supervision. At the end of 1710 such a 
Board was constituted, with Newton as its chief 
member, to examine the instruments at the Observatory 
and to put them into proper repair. A violent quarrel 
broke out between Newton and Flamsteed- the latter 
resenting any interference with his job, in which he 
had been working for over thirty years, with only one 
hundred pounds per annum to cover salary, instru- 
ments, running expenses, etc. Newton lost his temper, 
and Flamsteed's subsequent behaviour was almost 
vandalistic. The scientific contact between Newton 
and Flamsteed did not survive this shock ; they hardly 
corresponded again till Flamsteed's death in 1719. In 
any case, Newton had obtained sufficient information 
about the moon for his purposes namely, a second 
edition of the " Principia." 

This work had become so scarce that Newton had 
more than once been asked by Bentley to allow him 
to reissue it. Newton had made a number of notes 
in the margin of a copy of the first edition, and in 


June, 1708, he sent this to Bentley, who at once 
proceeded with having the work reprinted. But 
Bentley became involved in quarrels at Trinity and 
Newton was too busy to see to the printing himself. 
In the following year a brilliant young mathematician, 
Roger Cotes, a fellow of Trinity College, who had been 
appointed the first occupant of the Plumian Chair in 
astronomy and experimental philosophy at the early 
age of twenty-five, was entrusted with the task of 
preparing the second edition of the " Principia." 
Newton still had some corrections and additions to 
make and in October, 1709, Cotes received Newton's 
corrected copy through William Whiston. Newton 
was busy moving into a new residence in Chelsea when 
he had the satisfaction of hearing from Bentley : 
" You need not be so shy of giving Mr. Cotes too much 
trouble. He has more esteem for you, and obligations 
to you, than to think the trouble too grievous ; but, 
however, he does it at my orders, to whom he owes 
more than that, and so pray you be easy as to that. 
We will take care that no little slip in a calculation 
shall pass this fine edition. . . ." 

The choice of Cotes was a happy one. He set 
himself to the task with energy and with insight. He 
was not content to " print by the copy sent him," as 
Newton had suggested, but to produce a properly 
edited work. He consulted with Newton over and 
over again as the work of printing went on, and the 
long correspondence between Newton and Cotes con- 
stitutes one of the most valuable sets of scientific letters 
extant. Several additions were incorporated in the 
new edition of the " Principia " ; as Newton wrote in 
his preface : "In the Third Book the theory of the 
moon, and the precession of the equinoxes, are more 
fully deduced from their principles, and the theory of 
comets is confirmed by several examples, and their 
orbits more accurately computed." 


The production of the second edition of the 
"Principia" occupied four years (1709-1713). In 
1710 Newton changed his residence again, moving to 
St. Martin's Street, which runs into Leicester Square. 
The house he took was the first one on the left as one 
enters the street from the square : it was of some size 
and in a suitable position for one who was continually 
receiving visits from distinguished Englishmen and 
foreigners. His niece, Catherine Barton, had by now 
attracted the attention and admiration of numerous 
famous men like Dean Swift and Charles Montague 
the latter had become Earl of Halifax, and is said to 
have wanted to marry her ; but Miss Barton remained 
unmarried for some years yet and still served Newton 
as the leading figure in his household. Newton himself 
was already an old man, nearly seventy years of age. 
He was never above middle size, and tended to corpu- 
lency as he grew older. He was in good health, but 
somewhat clumsy in his attitudes. He was always 
friendly, but being continually steeped in meditation 
he spoke but little in company. He was by no means 
eccentric, but he was as apt to be remiss in his social 
duties as negligent of his own comforts. That lie 
sometimes sat in bed forgetting to dress himself 
through absorption in some problem merely proves 
him as human as all of us, not as human, indeed, as 
Descartes who, at one period of his life, spent most of 
his time in bed. If Newton sometimes thought he 
had fed when some kind friend had eaten his lunch 
for him, it only proves that he was no slave to food, 
just as he had remained free of the serfdom to snuff 
and tobacco. 

In 1711 Newton published an important paper on 
mathematical computation, the " Methodus Differen- 
tialis," containing formulae that have not lost their 
importance to this day. But a storm was brewing 
that was soon to break over Newton's head with great 


violence. His negligence with respect to his discovery 
of fluxions was bringing its punishment in its train. 

As early as 1699 a Swiss mathematician, Facio de 
Duillier, had somewhat clumsily broken a lance in 
defence of Newton's priority in the discovery of 
fluxions. " Compelled by the evidence of facts/' he 
said, " I hold Newton to have been the first inventor 
of the calculus, and the earliest by several years. And 
whether Leibnitz, its second inventor, has borrowed 
anything from him, I would prefer to my own judg- 
ment that of those who have seen the letters of Newten 
and copies of his other manuscripts." When Newton's 
" Optics " appeared and the reviewer in the " Acta 
Eruditorum" who was, in fact, Leibnitz himself, 
under the cloak of anonymity implied that Newton 
had plagiarized Leibnitz, the fury of English mathe- 
maticians was roused. John Keill of Oxford replied 
in 1708, and insinuated quite plainly that Leibnitz 
had obtained his differential calculus from some of 
Newton's manuscripts to which he had been allowed 
access. When Leibnitz read this he sent a strong 
protest to the Royal Society and asked that body to 
make Keill disown publicly the implied accusation. 
Keill did not disown his remarks, but drew attention 
to the review in the " Acta Eruditorum," and explained 
that from what Leibnitz saw of Newton's letters to 
Oldenburg he could discover the idea of the calculus. 
Leibnitz was not satisfied, and in December, 1711, he 
stated openly that the views expressed by the reviewer 
of the " Optics " had been only fair and just. 

It was now open war : not only was Keill involved 
but the Royal Society and its President, Newton, were 
thus dragged into the dispute. It was a very un- 
pleasant affair as all disputes involving personalities 
must be. Attempts have been made to give deep 
motives to the disputants and recondite causes to the 
bitterness of feeling evinced. One theory is that 


Leibnitz and Newton were really engaged in a political 
quarrel that Newton was a fanatical Tory, and as 
such opposed to the Elector of Hanover, so that 
Leibnitz naturally also shared in this displeasure. 
This pretty theory is, however, inconsistent with 
Newton's being " the glory of the Whig party," in the 
words of Macaulay, and extraordinarily friendly with 
the Elector of Hanover when he became King of 
England only a few years later, especially with the 
Princess of Wales, who was a particular friend of 
Leibnitz. No : it is not necessary to invent such 
impossible theories. Newton and Leibnitz were great 
men but only men, subject to the passions and failings 
of the species. 

The Royal Society had to take some action, and in 
March, 1712, a committee was appointed to examine 
all available documents and to express an opinion as 
to the independence and priority of the discovery of 
the calculus idea and method by Newton and Leibnitz. 
It is a great pity that Newton was himself President 
at the time an obvious charge of partiality and 
prejudice lay at the door of the committee and would 
discount much of the value of its decision. Among 
the members were Halley and the mathematicians 
Machin, de Moivre and Brook Taylor great names 
indeed as well as the Prussian Minister and others. 
There can be little doubt that the committee tried to 
be as impartial as possible : at the same time it is 
clear that it was not an independent jury, but rather 
a body appointed to vindicate Newton. 

Halley had been many things since Newton had 
come to London. Newton helped him to a post in one 
of the branch mints. Halley then undertook various 
scientific voyages, and finally became Savilian professor 
of geometry at Oxford. It was in his handwriting 
that the report of the committee was presented. After 
giving a brief history of the various papers and letters 


written by Newton the committee reports : " That 
the differential method is one and the same with the 
method of fluxions, excepting the name and mode of 
notation. . . . And therefore we take the proper 
question to be, not who invented this or that method, 
but who was the first inventor of the method. , . . 
For which reasons we reckon Mr. Newton the first 
inventor ; and are of opinion that Mr. Keill, in asserting 
the same, has been noways injurious to Mr. Leibnitz. 
And we submit to the judgment of the Society, whether 
the extracts, and letters, and papers, now presented, 
together with what is extant to the same purpose, in 
Dr. Wallis* third volume, may not deserve to be made 

It must be said in all fairness that the committee's 
report was a very balanced and reasonable one. Its 
suggestion to print the " extracts, letters and papers " 
was adopted, and in 1713 there appeared the " Com- 
mercium Epistolicum " or Correspondence with John 
Collins and others concerning the development of the 
method of the calculus. 

When Leibnitz heard of this publication he became 
furious, and a very acrimonious correspondence ensued, 
in which Leibnitz as well as the great John Bernoulli 
figured very unsatisfactorily, while Keill, acting no 
doubt under Newton's directions, laboured valiantly 
in defence and offence. Meanwhile, the second edition 
of the " Principia " appeared in 1713, and a second 
edition of the " Optics " in 1714. An attempt was 
made by Tory intriguers to remove Newton from the 
Mint by the offer of a very liberal pension : Newton 
declined, and remained in active charge of this institu- 
tion. His opinions were sought after on matters 
of moment to the country, and when Queen Anne 
died in 1714 and was succeeded by the Elector of 
Hanover as King George I the " honest blockhead " 
who punished so brutally in his cousin-wife the sin 



that he himself practised so flagrantly Newton 
remained a favourite at court. The King's son, 
George, was declared Prince of Wales ; the Princess 
of Wales was the accomplished Caroline of Anspach, 
who had regular evenings when distinguished men of 
science and learning visited her salon. Needless to 
say, Newton was an especially welcome visitor on such 
and other occasions. 

The weary quarrel over the calculus dragged on. 
The new editions of the " Principia " and the " Optics," 
and the succession of the Hanoverian house to the 
English throne, suggested to Leibnitz a new weapon 
of attack. One of the most important changes in the 
second edition of the " Principia " was a general 
scholium at the very end of the work. Here Newton 
points out very forcibly the inadequacy of the vortex 
theory of Descartes, and then proceeds to a semi- 
scientific, semi-theological disquisition on the nature 
of God, finishing with a slight reference to his ether 
theory of gravitation. To the new " Optics," too, 
Newton added a number of " queries " containing 
views and speculations on the constitution of matter 
in its various manifestations, on gravitation, etc. 
Leibnitz pounced upon these things as a means of 
discrediting his enemy. He had already, in 1710, 
attacked Newton's theory of gravitation as introducing 
the occult and the miraculous into natural philosophy. 
He renewed this attack towards the end of 1715, and 
directed his arguments to the Princess of Wales. He 
declared that philosophy and natural religion had 
decayed among the English, and accused Newton of 
materializing the conception of God and limiting His 

At the instance of the King, Newton now intervened 
personally in the dispute. This led Leibnitz to yet 
another attempt to overcome Newton. He challenged 
Newton in 1716 to solve a problem which is only 


soluble by a person in complete possession of the ideas 
and methods of the calculus. Newton solved the 
problem one evening after returning from his duties 
at the Mint. The dispute would perhaps have dragged 
on indefinitely, but Leibnitz' death in November, 1716, 
put a stop to the quarrel in the sense at least that 
Leibnitz was silenced and the Englishmen had it all 
their own way. 

Gottfried Wilhelm Leibnitz was three or four years 
younger than Newton. He was a man of remarkable 
genius as an administrator, diplomat, philosopher and 
mathematician. He was the outstanding German 
savant of his day, a man who has left his mark on 
metaphysical inquiry and in pure mathematics. His 
mathematical genius was for analytical form rather 
than for the geometrical and physical intuition in 
which Newton excelled. To him the calculus was 
more of a mathematical exercise with a beautiful 
notation to Newton it was a rugged tool, practical 
and penetrating. Newton realized the ideas better, 
Leibnitz devised the polished processes. 

This makes the dispute all the more regrettable. 
The effect of the dispute was to produce an estrange- 
ment between the British mathematicians and their 
continental colleagues. Newton's successors in England 
tried to follow his geometrical methods. They failed 
to make any real progress, and the Cambridge school 
of mathematics declined and practically died with 
Newton. Cambridge became the home of mathe- 
matical teaching with an examination tradition that 
evolved into the Mathematical Tripos : but it was not 
till a century after the end of the Newton-Leibnitz 
controversy that Cambridge mathematicians began 
to show signs of originality and fertility and this 
happened only when the prejudice against the conti- 
nental Leibnitzian notation and methods was overcome 
and the slavish imitation of Newton abandoned. 


Newton and Leibnitz were independent thinkers 
and discoverers. It was Newton's own fault and the 
fault of Barrow, Collins and other friends of his youth, 
that he was embroiled in controversy over the calculus. 
It is a recognized principle that priority is decided by 
the date of publication, and not by the date of dis- 
covery in the privacy of one's study. This was 
acknowledged in Newton's time, too. Nobody denied 
to Hadley the merit of and credit for the sextant, 
although Newton had invented it thirty years earlier : 
Hadley made the discovery public and reaped the 
reward. Why should not the prior publication by 
Leibnitz have been treated in the same manner ? 
Newton had too little respect for his own mathematical 
powers, and lived to regret it. 

During the progress of the calculus controversy 
Newton suffered two severe losses of friends whom he 
esteemed highly, Charles Montague, Earl of Halifax, 
and Roger Cotes. The former had reached the highest 
positions in the State and had done much to re-estab- 
lish English finance. He started the National Debt 
and the Bank of England, and reformed the currency 
with Newton's help. He had been first minister of 
the Crown under King William III, and although 
forced to retire from much of his public life when the 
Tories were the dominant power in the land, he emerged 
again as first minister of the Crown under George I. 
His death occurred in May, 1715. He had been a 
widower for some time some say that he had desired 
to marry Newton's niece and he bequeathed one 
hundred pounds to Newton as a mark of honour and 
esteem, and five thousand pounds with various other 
benefits to Catherine Barton " as a token of sincere 
love, affection, and esteem I have long had for her 
person, and as a small recompense for the pleasure and 
happiness I have had in her conversation." 

Halifax was only fifty-four years of age when he 


died. Even severer and more tragic was the death of 
Roger Cotes in 1716, who was taken away when not 
yet thirty-four years old. " If Mr. Cotes had lived," 
Newton said, " we might have known something. 11 

Two years after the death of her admirer, Halifax 
whether this is significant or not, one cannot say 
Catherine Barton, then thirty-eight years of age, 
married John Conduitt, a friend of Newton's, nine 
years her junior, who enjoyed independent means and 
was a member of Parliament. A year later Newton 
had the joy of welcoming into the world a grand-niece, 
Catherine Conduitt, who later became Viscountess 
Lymington and ancestress of the family of the Earl 
of Portsmouth. 

A semi-domestic event which must have given 
Newton much pleasure was the elevation of Halley to 
the position of Astronomer Royal in 1720 : no doubt 
Newton had a share in making this appointment. 
Halley was Secretary of the Royal Society since 1713, 
so that Newton had a great source of satisfaction 
in the scientific career of this sincere friend and 

Newton was now nearly eighty years of age. He 
was not frail or obviously aged. We have a portrait 
of him at the age of eighty-three, and even then he 
looked well a venerable sight with fine silver-white 
hair. He never became bald, never wore glasses, and 
enjoyed the use of his own teeth to the end. His mind 
was lively and alert, and he carried out his official 
duties at the Mint and his functions as President of 
the Royal Society without interruption. But in 1722 
Newton began to suffer from the infirmities of old age. 
It \as an affection of the bladder, which turned out 
to be much less serious than at first appeared. But 
Newton had to take special precautions with his food, 
to give up exciting dinner parties, and to give up the 
use of his carriage, since jerking motion was liable to 


produce another attack. In this way he remained 
tolerably well for about two years. 

Newton used this respite for a very important 
purpose. A third edition of the " Principia " was 
needed. It is remarkable that for each edition of this 
great work Newton enjoyed the inestimable advantage 
of the printing being carried out under the direct 
supervision of a young and energetic man of learning 
and talent. Halley was only thirty years of age when 
he brought out the first edition in 1687 ; Cotes was 
barely thirty-one years of age when he brought out 
the second edition in 1713. For the third edition 
Newton secured the help of another brilliant young 
scientist, Henry Pemberton, who began the task in 
1722 when he was twenty-nine years old, and published 
the third edition in 1726 when he was barely thirty- 

Henry Pemberton was a young doctor who had 
become acquainted with the " Principia " when still 
a medical student. This made him turn his attention 
to mathematical studies, and he became acquainted 
with Newton, who recognized in some of Pemberton's 
work considerable mathematical power. The old 
scientist and the young doctor became great friends 
and finally the latter undertook to issue the new edition 
of the " Principia. 1 ' 

Pemberton, like Cotes, was not an editor in the 
restricted sense. He discussed with Newton every 
point that required consideration during the course of 
the printing, and did everything with the knowledge 
and approval of his senior. Meanwhile more obvious 
signs of physical decay made themselves manifest in 
Newton. In August, 1724, he suffered from stone in 
the bladder and in January, 1725, he was attacked by 
inflammation of the lungs, accompanied by severe 
coughing, followed a month later by gout in both feet. 
The air of the Leicester Square district was not 


considered good for him, and Newton moved to Orbell's 
Buildings, now called Pitt's Buildings, in Pitt Street, 
near High Street, Kensington. The change did him 
some good, but he felt that he ought to give up his 
duties at the Mint. He wanted, apparently, to keep 
the Mastership in the family, as he tried to get Conduitt 
appointed Master. But this did not materialize, and 
Newton remained Master but Conduitt did most of 
his work there ! Newton continued to preside at the 
Royal Society, but it is on record that he fell asleep 
while occupying the chair. 

Newton always befriended mathematical genius he 
encouraged and helped men like Cotes, Duillier, David 
Gregory and Pemberton. In 1725 two Scotch mathe- 
maticians received marks of his approval and his kindly 
help. Colin Maclaurin was one of the greatest mathe- 
maticians that Scotland has produced. In 1717, at 
the early age of nineteen, he was appointed professor 
of mathematics at the Marischal College, Aberdeen. 
But Maclaurin desired to go to Edinburgh, and to 
obtain the reversion of the chair held by James Gregory 
the nephew of the inventor of the reflecting telescope. 
It was Newton's recommendation that in 1725 secured 
for Maclaurin the post of assistant and successor to 
Gregory, and he even offered to contribute twenty 
pounds per annum to the salary of the assistantship 
in order to make the arrangement feasible. Maclaurin 
became professor a year later. 

James Stirling was a brilliant young Oxford student 
of mathematics. In 1715, when twenty-three years of 
age, he got embroiled with Jacobites and had to flee. 
He went to Venice and soon began to publish important 
work on geometry. Newton not only got Stirling's 
work published in England, but in 1725 obtained 
permission for him to return to England. Stirling 
had an interesting career in Scotland, finishing off as 
the manager of a coal-mine. Newton's approval of 


Maclaurin and Stirling has been more than endorsed 
by posterity. 

The third edition of the " Principia " was meanwhile 
going ahe3d, and early in 1726 it appeared, containing 
an excellent portrait of Newton at the age of eighty- 
three. Newton's generosity to Pemberton was both 
moral and material. He presented him with a sum 
of two hundred guineas (he had already given a 
hundred guineas to the astronomer Pound, whose 
observations Newton used in the new edition) and 
paid him a high compliment in the preface. Nobody 
ever could complain of Newton as regards personal 
generosity. He even remembered to contribute to- 
wards the cost of repairing the floor of Colsterworth 

The issue of the third edition of the " Principia " 
was the end of Newton's scientific work. 

THE END, 1727 

I do not know what I may appear to the world ; but to myself 
I seem to have been only like a boy playing on the sea-shore, and 
diverting myself in now and then finding a smoother pebble or a 
prettier shell than ordinary, whilst the great ocean of truth lay all 
undiscovered before me. 


A REMARKABLY useful and well-spent life 
was drawing to a close. The great worker and 
thinker felt that the end was near. His calm 
objectiveness in scientific judgment never deserted 
him. Conscious of the unprecedented progress that 
he had made in the understanding of Nature's laws, he 
was, nevertheless, ever ready to revise his views when 
facts seemed to go against them. When, a few months 
before his death, he was threatened with the complete 
demolition of his structure based on universal gravita- 
tion, his reply was simply : " It may be so, there is no 
arguing against facts and experiments." Two centuries 
have passed and the structure stands firmer than ever. 
The last years of Newton's life were occupied with 
another interest. The study of chronology is a natural 
occupation for a mathematician, and several great 
mathematicians have worked at it : the different races 
and religions of humanity have seen to it that sufficient 
confusion exists to puzzle the most ingenious. Newton 
had often read history and chronology as a mental 
recreation, and he was induced by the Princess of 
Wales to write a brief account of his own views of the 
correlation between the dates ipf events in ancient 
history. When [Newton found m 1725 that this had 


got into print without his permission, he decided to 
prepare a large work on the subject. The " Chronology 
of Ancient Kingdoms " was completed only a short 
time before his death and was not published till a 
year after his death/) 

In August, 1726, further physical ailments attacked 
Newton. He was confined to his house at Kensington, 
and spent much of his time in reading, especially the 
Bible. On Tuesday, February 28, 1727, he felt, as he 
thought, well enough to go to Crane Court, near Fleet 
Street, London to preside at the Royal Society on Thurs- 
day, March 2nd. He went, and came back to Kensing- 
ton on Saturday, March 4th, seriously ill. This was the 
beginning of the end. A week later the illness was 
diagnosed as stone in the bladder, and it was felt that 
death was near. Newton suffered excruciating pains, 
but he bore them patiently and uncomplainingly. In 
the intervals he conversed cheerfully, and on Wednes- 
day, March I5th, there appeared to be some improve- 
ment in his condition. This was an illusion, however. 
On Saturday evening, March i8th, he had a relapse 
and became insensible. He remained like this till 
after midnight of the following day, ano&ied painlessly 
between one o'clock and two o'clock in the morning 
of Monday, March 20, 1727/1 

Newton died in his ei^t^fifth year. The highest 
possible posthumous honours were done him. His 
body lay in state in the Jerusalem Chamber on Tuesday, 
March 28th, and was buried in Westminster Abbey. 
A plain flagstone marks the actual grave with the 
inscription " Hie depositum est Quod Mortale fuit 
Isaaci Newtoni." A monument dedicated to Newton's 
memory was erected in 1731, when also a medal was 
issued at the Mint in his honour. 

Newton left his family estates at Woolsthorpe and 
Sewstern to the heir-at-law, the ne'er-do-well, John 
Newton, his second cousin. He had already in his 

THE END, 1727 155 

lifetime made ample provision for more distant relatives 
like the Ayscoughs, and for such nearer relations as 
were beyond the scope of his bequests by will. His 
personal estate of thirty-two thousand pounds went to 
his eight living nephews and nieces, the three children 
of his stepbrother, Benjamin Smith, the three children of 
his stepsister, Mary Pilkington, and the two daughters 
of his stepsister, Hannah Barton. The Mastership of 
the Mint went to John Conduitt after all. 

The impression that Newton made on British 
scientific life, and on the scientific life of humanity as 
a whole, has remained one of the indelible imprints 
on the sands of time. It was only after his death, as 
generation after generation of the mightiest intellects 
of Europe followed out his ideas, and triumph after 
triumph was scored in the elucidation of Nature's 
puzzles, that the true greatness of his genius was 
appreciated. Rarely, if ever, have so many noble 
qualities been united in one man. A great experi- 
mentalist and manipulator, a profound mathematician 
and theorist, a clear and logical thinker, a fine exponent 
and writer, a practical national benefactor, a kind and 
appreciative supporter of merit and ability, a model 
relation to the members of his family, an example of 
unerring rectitude, an abhorrer of all vice and of 
cruelty to man and beast Newton has long since 
obtained absolution at the hands of posterity for the 
faults of temper which sometimes marred his personal 
relationships, and the faults of self-appreciation that 
ignored the mathematician in himself and sought in- 
spiration in the pseudo-science of alchemy. Humanity 
will ever rejoice to have counted Newton among its sons. 




Many editions of Newton's chief individual 
works, such as the " Principia " and " Optics " 
have appeared from time to time, and are easily 
obtainable. No really authoritative edition of 
his complete works has been issued yet. A col- 
lection of Newton's writings in five volumes was 
issued by Samuel Horsley in the years 1779-1785, 
under the title : Isaaci Newtoni Opera quae 
extant Omnia. 


Aberration, chromatic, 59, 60 

spherical, 54-7 
Academic life, 133 
Acceleration, 44 
Achromatism, 68 
" Acta Eruditorum," 108, 139, 


Action at a distance, 122 
Alchemy, 125, 155 
Algebra, 65, 139 
Anne, Queen, 135, 137-8, 145 
Apocalypse of St. John, 125 
Apple, 45, 46 
Apples for cider, 82 
Arabs, 32 
Areas, 21-3 
Aristotle, 43 
Astrophysics, 73 
Attraction of sphere, no 
Authority, 43, 69, 71, 79 
Ayscough, 5, 7, 155 

Bacon, Roger, 3 

Barrow, Isaac, 58, 64-5, 148 

Barton, Catherine, 9, 132, 142, 


Bentley, Richard, 125-6, 140-1 
Bernoulli, James, 135 
Bernoulli, John, 134-5, 145 
Binomial Theorem, 16-8, 26 
Bohr, Niels, 73 
Boyle, Robert, 26, 74, 78, 101, 


Brachistochrone, 134 
Bradley, James, 77 
Brahe, Tycho, n, 38-9, 43, no 
Brigstock, 132 
Burton Goggles, 7 
Byron, Lord, xii 

Calendar, 4-5, 135 

Cambridge, 16, 123, 138, 147 
Caroline of Anspach, Princess of 

Wales, 144, 146, 153 
Cartesian ovals, 56, 60, 
Cassini, Giovanni Domenico, 114 
Cavalieri, Bonaventura, 25 
Central acceleration, 48-9, 83, 


Centre of gravity, 106-7, JI 4 
Charles I, i, 2 

Charles II, i, 65-6, 71, 90, 92-3 
Christ's Hospital, 134 
Chronology, I53~4 
Clark, apothecary, 7 
Coinage, 130 

Collins, John, 64-5, 145, 148 
Colour, 29, 53, 57-8, 67, 78, 139 
Colsterworth, 2, 5, 152 
Comets, 9, 88, 90, 93, 117, 119- 


Commercium Epistolicum, 145 
Conduitt, John, 149, 151, 155 
Conduitt, Catherine, Viscountess 

Lymington, 149 
Comes, 38-9, 108, 117 
Cooling, law of, 135 
Copermcan system, 37, 40-1 
Copernicus, Nicolas, 10, 35-8, 41, 

Corpuscular theory of light, 77, 


Cotes, Roger, 141, 149-51 
Cromwell, Oliver, 2, 3, 10 
Cubic Curves, 139 
Cycloid, 134 

De Duillier, Facio, 143, 151 

Deferent, 32, 35-6 

De Moivre, Abraham, 144 

De Motu, 91, 94. *7 

De Mundi, 96, 107, 112, 117 




De Revolutionibus Orbium 

Coelestium, 38 
Descartes, Rene, 16, 42, 56-8, 

122, 142, 146 
Diamond, 127 
Differential Calculus, 82, 108, 

i39, 143 

Diffraction, 78, 139 
Discs of planets, 37 
Dispersion, 59, 68-9 
Dispute with Leibnitz, 1437 

Earthly and celestial, 33, 38, 93, 


Earth, motions of, 35-6, 85, 87 
Eclipse, 118 
Edinburgh, 123, 151 
Einstein, Albert, 73, 119 
Elasticity, 45 
Electricity, 81 
Ellipse, 39, 40, 83-4, 90, 117, 


England, 122, 136 
Epicycle, 32, 35-6, 38 
Ether, 42, 77-9, 122, 146 
Exhaustions, method of, 23 

Falling body, 44, 86 

Fermat, Pierre de, 25 

Fire, 127 

Fits, 76-8, 139 

Fixed stars, 106 

Flambteed, John, 88, 93, 101, 

114, 128-9, 134, 137, 140 
Flattening of earth and planets, 

94, in, 114 
Fluids, in 
Fluxions, 19, 21-2, 27, 43, 64, 

70, 81-2, 107-8, 125, 139, 143 
Foucault, Jean Bernard Leon, 77 
French Academy, 135 
Fresnel, Augustin Jean, 79 

Gale, experiments in, 10 
Galilei, Galileo, 37, 42-4, 46, 53, 

56-8, 105 
George, Prince of Denmark, 

Prince Consort, 137, 140 

George I, Elector of Hanover, 


George, Prince of Wales, 146 
Grantham, 2, 7, 10, u, 99 
Gravitation, 42, 73, 78, 81, 

8 3~4. 93, 113, H9> 122, 125, 


Greeks, 33, 38 
Gregory, David, 151 
Gregory, James, 60, 63 
Gregory, James (the younger), 


Grimaldi, 78 
Gyroscope, 114 

Hadley, John, 135, 148 

Halos, 53, 139 

Halley, Edmund, 89-91, 94-6, 

101, 119-21, 123-4, 1-2 8-9, 

144, 149, 150 
Hero worship, 79 
Hcrschel, William, 126 
Homer, 44 
Hooke, Robert, 45, 69, 74, 77-9, 

82-4, 86-90, 95-6, 99, 139 
Huygens, Christian, 69, 77, 79, 

" Hypotheses," 113 

Interference, 77 

Inverse square law, 45, 47, 49, 
50, 83-4, 87-8, 90-2, 96, 114 

James II, 97, 101, 123, 137 
Jeffreys, Judge, 98, 121 
Jews, 32 

Kant, Immanuel, 126 

Kcill, John, 143, 145 

Kepler, John, n, 25, 38-42, 48, 

57, 104, no 
Kepler's Laws, 40-1, 48-9, 84, 

87, 90, 113 

King's College, Cambridge, 124 
King's School, Grantham, 2, 7, 

Lagrange, Joseph Louis, 118 



Laplace, Pierre Simon, 102, 118, 


Latent heat, 136 
Laws of motion, 42-3, 45, 92, 

103-4, 109 
Leibnitz, Gottfried Wilhelm, 82, 

99, 108, 122, 125, 135-6, 139, 


Librations of moon, 81, 114 
Locke, John, 124, 127, 129 
London. 16 
Lucas, 68 
Lucretius, Titus Cams, 126 

Macaulay, Lord, 123, 131, 135, 


Machm, John, 144 
Maclaurin, Colin, 151-2 
Market Overton, 5 
Mars, 38-9 
Mary II, 123 
Masses, ti8 

Mathematical Tripos, 147 
Mcrcator, Nicolas, 81 
Mercury, 48, 119 
" Methodus Diff erentialis, " 142 
Milton, John, 102 
Mint, Royal, 16, 131-3, 151, 155 
Monochromatic light, 74 
Montague, Charles, Earl of 

Halifax, 124, 129-32, 142, 

Moon, 30-1, 37, 88, 101, 113, 

115-6, 127-8, 134 
Moon's distance, 36, 50 
Moon's motion, 46, 50-1, 89, 93 

Nature, benevolence of, 105, 107, 


Nebular hypothesis, 126 
Neptune, 119 

Neville's Court, Trinity, 112 
Newton, Humphrey, 99 
Newton, Isaac : 

birth, 2, 4 

family, 5, 9, 155 

baptism, 5 

grandmother, 7 

Newton, Isaac (contd.) : 
school, 8 
games, 9 
farmer, 10 

back at school, Miss Storey, n 
Trinity College, Cambridge, 

12, 15, 19, 62 
scientific character, 15, 16, 47, 

5*> 77,92, 99, 129, 155 
B.A. f 19 

plague, 21, 29, 53, 62 
falling apple, 45 
optics, 60, 62, 66-7, 74-6, 78 
gravitation, 60, 81 
Fellow of Trinity, 62-3 
MA, 63 

reflecting telescope, 6j, 65, 67 
Lucasian professor, 64-5 
fluxions, 64 

Fellow of Royal Society, 66 
neglect of food and sleep, 70, 

99, 126 
excused holy orders, 71, 92, 

excused fees by Royal Society, 

Wave-theory of light ; theory 

of fits, 76-7 
Hooke, 82 
Halley, 90-1, 94 
writes "De Motu," 91 
" Prmcipia," 94, 101, 122-3, 

125, 140-2, 145-6, 150, 152 
writes " De Mundi," 96 
bachelor life, 98-9, 124, 126 
lectures, 99 
garden, 100 

Leibnitz, 82, 122, 143-7 
Parliament, 123, 135, 138 
Charles Montague, 124, 129 - 

32, 142, 148 
mother's death, 124 
lack of recognition, 124 
theology, 125 
unwell, 126-7 
story of dog Diamond, 127 
Locke, 129 
Warden of Mint, 131 
Master of Mint, 132 
money matters, 132, 155 
residences, 132, 142, 151 



Newton, Isaac (contd.) : 

niece, Catherine Barton, 9, 


solves problems, 134, 147 
offered pension by French 

king, 134 
elected to French Academy, 


resigns fellowship and chair, 

President of Royal Society, 


life in London, 137 
knighted by Queen Anne, 138 
proposes marriage, 138 
Roger Cotes, 141 
refuses to retire from Mint, 


mathematics, 147, 155 
John Conduitt, 149, 151, 155 
illnesses, 149, 150 
Henry Pemberton, 150-2 
on himself, 153 
last illness, death, and burial, 

Newton, John, heir-at-law, 7, 


Newton's rings, 746 
Norris, Lady, 138 
North Witham, 5 

Oldenburg, Henry, 66, 68, 82, 

96, 143 

" Optics," 79, 138-9, 143, 145-6 
Orthodoxy, Christian, 126 
Oscillatory motion, no 
Oxford, 1 6, 123, 143-4, 151 

Paget, 101 
Parabola, 117 

Parliament, i, 3, 123, 135, 138 
Pemberton, Henry, 150-2 
Pendulum, in, 114 
Pepys, Samuel, 96, 124 
Periodicity in light, 76-7 
Perturbations, 109, no, 115 
Phases of Venus, 37 
Picard, Jean, 84, 89 
Planets, 31 

Plague, Great, 21, 29, 53, 62 
Plato, 126 

Portsmouth family, 149 
Pound, 152 

Precession, 93, in, 114 
Principia, 94, 101, 122-3, 125, 

140-2, 145-6, 150, 152 
Priority, 148 
Prism, 19, 53, 57-9 
Prophecies of Daniel, 125 
Ptolemaic system, 31-2 

Queries in " Optics," 146 

Radius of earth, 50, 52, 84, 89 
Rates of change, 22 
Reflecting telescope, 53, 60, 63, 
65, 67, 83 

microscope, 67 
Refraction, astronomical, 128 
Relative motion, 36, 105 
Relativity, 73, 119 
Resisting medium, in 
Roemer, Olaus, 135 
Royal Observatory, Greenwich, 

13. 92-3, 140 
Royal Society, 13, 65-6, 92, 94, 

96, 136, 140, 143-4, 149, 151 

St. Andrews, 123 
Satellites, 37, 93, 113, 115 
" Scholia," 107 
Sewstern, 5, 71, 154 
Sextant, 135, 148 
Shakespeare, William, i, 3 
Skillmgton, 7 
Smith, Barnabas, 5 
Sound wave, in 
Space and time, 103 
Spectrum, 53, 67, 73, 139 
Stirling, James, 151-2 
Stoke, 7 

Stoke Rochford, 7, 45 
Storey, Miss, 11 
Sun, 30-1, 37, 88, 114, 116 
Swift, Dean, 142 

Taylor, Brook, 144 
Telescope, 53-4, 60, 63, 65-67 



Theology, 125-6, 146 
Thin films, 74 
Tides, 93-4, IIT, 115-6 
Transparency and opacity, 78 
Turnor, Edmund, 7 

Uniform circular motion, 33, 38, 


Unity in universe, 49 
" Universal Arithmetic," 140 
Universities, 97 
Uranus, 118 

Volume, 25 

Vortex Theory, 42, 112, 122, 

Wallis, John, 25, 108, 125, 145 
Wave-theory, 69, 77, 79 
Whiston, William, 135, 139, 141 
William III, 123, 131, 135, 137 
Woolsthorpe, 2, 45, 51, 71, 82-4, 

88-9, 154 
Wren, Christopher, 89, 90, 96, 

99, 137 

Young, Thomas, 79 






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